From 3be57a5a70fcc1aa45a2a31e19ab9ac89aab5b54 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Wed, 16 Oct 2024 18:35:19 +0200 Subject: [PATCH] Update website for recog 1.4.3 --- PackageInfo.g | 8 +- _data/package.yml | 26 +++--- doc/chap0.html | 6 +- doc/chap0.txt | 4 +- doc/chap0_mj.html | 8 +- doc/chap1.html | 8 +- doc/chap1.txt | 14 +-- doc/chap1_mj.html | 10 +-- doc/chap2.html | 2 +- doc/chap2_mj.html | 4 +- doc/chap3.html | 26 +++--- doc/chap3_mj.html | 28 +++--- doc/chap4.html | 8 +- doc/chap4_mj.html | 10 +-- doc/chap5.html | 6 +- doc/chap5_mj.html | 8 +- doc/chap6.html | 8 +- doc/chap6.txt | 2 +- doc/chap6_mj.html | 10 +-- doc/chap7.html | 2 +- doc/chap7_mj.html | 4 +- doc/chap8.html | 2 +- doc/chap8_mj.html | 4 +- doc/chap9.html | 2 +- doc/chap9_mj.html | 4 +- doc/chapBib.html | 208 +++++++++++++++++++++---------------------- doc/chapBib.txt | 72 +++++++-------- doc/chapBib_mj.html | 210 ++++++++++++++++++++++---------------------- doc/chapInd.html | 2 +- doc/chapInd.txt | 16 ++-- doc/chapInd_mj.html | 4 +- 31 files changed, 363 insertions(+), 363 deletions(-) diff --git a/PackageInfo.g b/PackageInfo.g index 18347f6e..3560a7ee 100644 --- a/PackageInfo.g +++ b/PackageInfo.g @@ -18,8 +18,8 @@ SetPackageInfo( rec( PackageName := "recog", Subtitle := "A package for constructive recognition of permutation and matrix groups", -Version := "1.4.2", -Date := "27/09/2022", # dd/mm/yyyy format +Version := "1.4.3", +Date := "16/10/2024", # dd/mm/yyyy format License := "GPL-3.0-or-later", ## Information about authors and maintainers. @@ -172,10 +172,10 @@ rec( FirstNames := "Max", IsAuthor := false, IsMaintainer := true, - Email := "horn@mathematik.uni-kl.de", + Email := "mhorn@rptu.de", WWWHome := "https://www.quendi.de/math", Place := "Kaiserslautern", - Institution := "TU Kaiserslautern" + Institution := "RPTU Kaiserslautern-Landau" ), rec( LastName := "Siccha", diff --git a/_data/package.yml b/_data/package.yml index 4e10f469..74c8c714 100644 --- a/_data/package.yml +++ b/_data/package.yml @@ -1,7 +1,7 @@ name: recog -version: "1.4.2" +version: "1.4.3" license: "GPL-3.0-or-later" -date: 2022-09-27 +date: 2024-10-16 description: | A package for constructive recognition of permutation and matrix groups @@ -74,9 +74,9 @@ packageinfo: https://gap-packages.github.io/recog/PackageInfo.g downloads: - name: .tar.gz - url: https://github.com/gap-packages/recog/releases/download/v1.4.2/recog-1.4.2.tar.gz + url: https://github.com/gap-packages/recog/releases/download/v1.4.3/recog-1.4.3.tar.gz - name: .tar.bz2 - url: https://github.com/gap-packages/recog/releases/download/v1.4.2/recog-1.4.2.tar.bz2 + url: https://github.com/gap-packages/recog/releases/download/v1.4.3/recog-1.4.3.tar.bz2 abstract: | @@ -95,29 +95,29 @@ keywords: | group recognition, matrix group recognition, permutation group, black box group, composition tree, Aschbacher classes, method selection. citeas: |

- [NSH22] Neunhöffer, M., Seress, Á. and Horn, M., + [NSH24] Neunhöffer, M., Seress, Á. and Horn, M., recog, A package for constructive recognition of permutation and matrix groups, - Version 1.4.2 - (2022)
+ Version 1.4.3 + (2024)
(GAP package), https://gap-packages.github.io/recog.

bibtex: | - @misc{ recog1.4.2, + @misc{ recog, author = {Neunh{\"o}ffer, M. and Seress, {\a'A}. and Horn, M.}, title = {{recog}, A package for constructive recognition of - permutation and matrix groups, {V}ersion 1.4.2}, - month = {Sep}, - year = {2022}, + permutation and matrix groups, {V}ersion 1.4.3}, + month = {Oct}, + year = {2024}, note = {GAP package}, howpublished = {\href {https://gap-packages.github.io/recog} - {\texttt{https://gap-packages.github.io/}\discretionary + {\texttt{https://gap\texttt{\symbol{45}}packages.github.io/}\discretionary {}{}{}\texttt{recog}}}, keywords = {group recognition; matrix group recognition; permutation group; black box group; composition tree; Aschbacher classes; method selection}, - printedkey = {NSH22} + printedkey = {NSH24} } diff --git a/doc/chap0.html b/doc/chap0.html index 657e91ff..4c0a9432 100644 --- a/doc/chap0.html +++ b/doc/chap0.html @@ -29,10 +29,10 @@

recog

A package for constructive recognition of permutation and matrix groups

- 1.4.2

+ 1.4.3

- 27 September 2022 + 16 October 2024

@@ -333,6 +333,6 @@

Contents

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap0.txt b/doc/chap0.txt index 4ef71d04..64ecf4b2 100644 --- a/doc/chap0.txt +++ b/doc/chap0.txt @@ -6,10 +6,10 @@  A package for constructive recognition of permutation and matrix groups  - 1.4.2 + 1.4.3 - 27 September 2022 + 16 October 2024 Max Neunhöffer diff --git a/doc/chap0_mj.html b/doc/chap0_mj.html index c51ee00f..1661ac3d 100644 --- a/doc/chap0_mj.html +++ b/doc/chap0_mj.html @@ -6,7 +6,7 @@ GAP (recog) - Contents @@ -32,10 +32,10 @@

recog

A package for constructive recognition of permutation and matrix groups

- 1.4.2

+ 1.4.3

- 27 September 2022 + 16 October 2024

@@ -336,6 +336,6 @@

Contents

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap1.html b/doc/chap1.html index ca4d82e7..b695fac2 100644 --- a/doc/chap1.html +++ b/doc/chap1.html @@ -52,11 +52,11 @@

1.2 Overview over this manual

Chapter 2 describes the installation of this package.

-

Chapter 3 describes the generic, recursive procedure used for group recognition throughout this package. At the heart of this procedure is the definition of "FindHomomorphism" methods, which is also described in that chapter. For the choice of the right method for finding a homomorphism (or an isomorphism) we use another generic procedure, the "method selection" which is not to be confused with the GAP method selection.

+

Chapter 3 describes the generic, recursive procedure used for group recognition throughout this package. At the heart of this procedure is the definition of FindHomomorphism methods, which is also described in that chapter. For the choice of the right method for finding a homomorphism (or an isomorphism) we use another generic procedure, the method selection which is not to be confused with the GAP method selection.

Our own method selection system is described in detail in Chapter 4, because it is interesting in its own right and might be useful in other circumstances.

-

Chapter 6 describes the available "FindHomomorphism" methods.

+

Chapter 6 describes the available FindHomomorphism methods.

Chapter 5 explains what one can do with a completed recognition tree.

@@ -74,7 +74,7 @@

1.3 Feedback and support

1.4 Literature (temporary)

-

TODO Find the appropriate place to put these references, so that they appear in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLGLO13] [LGO09] [BLGN+05] [BLGN+03] [NP98] [NP99] [NP97] [Pra99] [CLG97a] [CLG97b] [CLGM+95] [BNS06] [CNRD09] [BHLGO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CLG98] [CLGO06] [CLG01] [CFL97] [DLGO15] [GH97] [GLGO06] [HLGOR96a] [HLGOR96b] [HR94] [IL00] [KM13] [KM15] [LGO97a] [LGO02] [LGO97b] [LG01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] [Pak00] [Par84]

+

TODO Find the appropriate place to put these references, so that they appear in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLLO13] [LO09] [BLN+05] [BLN+03] [NP98] [NP99] [NP97] [Pra99] [CL97a] [CL97b] [CLM+95] [BNS06] [CNR09] [BHLO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CL98] [CLO06] [CL01] [CFL97] [DLO15] [GH97] [GLO06] [HLOR96a] [HLOR96b] [HR94] [IL00] [KM13] [KM15] [LO97a] [LO02] [LO97b] [Lee01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] [Pak00] [Par84]

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
@@ -83,6 +83,6 @@

1.4 Literature (temporary)

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap1.txt b/doc/chap1.txt index d563c03b..e9759699 100644 --- a/doc/chap1.txt +++ b/doc/chap1.txt @@ -56,11 +56,11 @@ 1.4 Literature (temporary) TODO Find the appropriate place to put these references, so that they appear - in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLGLO13] [LGO09] [BLGN+05] - [BLGN+03] [NP98] [NP99] [NP97] [Pra99] [CLG97a] [CLG97b] [CLGM+95] [BNS06] - [CNRD09] [BHLGO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] - [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CLG98] [CLGO06] - [CLG01] [CFL97] [DLGO15] [GH97] [GLGO06] [HLGOR96a] [HLGOR96b] [HR94] [IL00] - [KM13] [KM15] [LGO97a] [LGO02] [LGO97b] [LG01] [LMO07] [NP92] [Nie05] - [O'B11] [O'B06] [Pak00] [Par84] + in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLLO13] [LO09] [BLN+05] + [BLN+03] [NP98] [NP99] [NP97] [Pra99] [CL97a] [CL97b] [CLM+95] [BNS06] + [CNR09] [BHLO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] + [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CL98] [CLO06] [CL01] + [CFL97] [DLO15] [GH97] [GLO06] [HLOR96a] [HLOR96b] [HR94] [IL00] [KM13] + [KM15] [LO97a] [LO02] [LO97b] [Lee01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] + [Pak00] [Par84] diff --git a/doc/chap1_mj.html b/doc/chap1_mj.html index db0819bd..285d2642 100644 --- a/doc/chap1_mj.html +++ b/doc/chap1_mj.html @@ -6,7 +6,7 @@ GAP (recog) - Chapter 1: Introduction @@ -55,11 +55,11 @@

1.2 Overview over this manual

Chapter 2 describes the installation of this package.

-

Chapter 3 describes the generic, recursive procedure used for group recognition throughout this package. At the heart of this procedure is the definition of "FindHomomorphism" methods, which is also described in that chapter. For the choice of the right method for finding a homomorphism (or an isomorphism) we use another generic procedure, the "method selection" which is not to be confused with the GAP method selection.

+

Chapter 3 describes the generic, recursive procedure used for group recognition throughout this package. At the heart of this procedure is the definition of FindHomomorphism methods, which is also described in that chapter. For the choice of the right method for finding a homomorphism (or an isomorphism) we use another generic procedure, the method selection which is not to be confused with the GAP method selection.

Our own method selection system is described in detail in Chapter 4, because it is interesting in its own right and might be useful in other circumstances.

-

Chapter 6 describes the available "FindHomomorphism" methods.

+

Chapter 6 describes the available FindHomomorphism methods.

Chapter 5 explains what one can do with a completed recognition tree.

@@ -77,7 +77,7 @@

1.3 Feedback and support

1.4 Literature (temporary)

-

TODO Find the appropriate place to put these references, so that they appear in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLGLO13] [LGO09] [BLGN+05] [BLGN+03] [NP98] [NP99] [NP97] [Pra99] [CLG97a] [CLG97b] [CLGM+95] [BNS06] [CNRD09] [BHLGO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CLG98] [CLGO06] [CLG01] [CFL97] [DLGO15] [GH97] [GLGO06] [HLGOR96a] [HLGOR96b] [HR94] [IL00] [KM13] [KM15] [LGO97a] [LGO02] [LGO97b] [LG01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] [Pak00] [Par84]

+

TODO Find the appropriate place to put these references, so that they appear in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLLO13] [LO09] [BLN+05] [BLN+03] [NP98] [NP99] [NP97] [Pra99] [CL97a] [CL97b] [CLM+95] [BNS06] [CNR09] [BHLO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CL98] [CLO06] [CL01] [CFL97] [DLO15] [GH97] [GLO06] [HLOR96a] [HLOR96b] [HR94] [IL00] [KM13] [KM15] [LO97a] [LO02] [LO97b] [Lee01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] [Pak00] [Par84]

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
@@ -86,6 +86,6 @@

1.4 Literature (temporary)

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap2.html b/doc/chap2.html index a7f9e24d..50a43438 100644 --- a/doc/chap2.html +++ b/doc/chap2.html @@ -39,6 +39,6 @@

2 Installation of the recogGoto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap2_mj.html b/doc/chap2_mj.html index d631a6d3..0b6aa137 100644 --- a/doc/chap2_mj.html +++ b/doc/chap2_mj.html @@ -6,7 +6,7 @@ GAP (recog) - Chapter 2: Installation of the recog package @@ -42,6 +42,6 @@

2 Installation of the recogGoto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

generated by GAPDoc2HTML

diff --git a/doc/chap3.html b/doc/chap3.html index 4337f7f8..493bcb85 100644 --- a/doc/chap3.html +++ b/doc/chap3.html @@ -88,15 +88,15 @@

3 Group recognition

The generic framework was designed having three situations in mind: permutation groups, matrix groups and projective groups. Although the methods used are quite different for those cases, there is a common pattern in the procedure of recognition. Namely, first we have to find a homomorphism, solve the constructive membership problem recursively in image and kernel, then put it together. The recursion ends in groups where we can solve the constructive membership problem directly. The general framework reflects this idea and separates it from the rest of the recognition methods.

-

Solution of the constructive membership problem comes in two stages: first a "recognition phase" and then a "verification phase". The recognition phase usually consists of randomised algorithms with certain error or failure probabilities. The result is some kind of "recognition information" that will describe the group already very well, but which is not yet proven to be correct. However, one can already write arbitrary elements in the group as product of the given generators. In the verification phase a presentation of the group is calculated, thereby proving that the group generated by the given generators is in fact isomorphic to the group described by the recognition information. In many cases the verification phase will be much more expensive than the recognition phase.

+

Solution of the constructive membership problem comes in two stages: first a recognition phase and then a verification phase. The recognition phase usually consists of randomised algorithms with certain error or failure probabilities. The result is some kind of recognition information that will describe the group already very well, but which is not yet proven to be correct. However, one can already write arbitrary elements in the group as product of the given generators. In the verification phase a presentation of the group is calculated, thereby proving that the group generated by the given generators is in fact isomorphic to the group described by the recognition information. In many cases the verification phase will be much more expensive than the recognition phase.

-

In the following sections, we describe the generic framework. We begin in Section 3.1 with a technical description of the recursive procedure behind our main function RecogniseGroup (3.1-5). In Section 3.2 we describe the return type of RecogniseGroup (3.1-5) which we call "recognition nodes". The methods to find homomorphisms are described in Section 3.3. Finally, we have three sections in which we collect conventions for the recognition of different types of groups.

+

In the following sections, we describe the generic framework. We begin in Section 3.1 with a technical description of the recursive procedure behind our main function RecogniseGroup (3.1-5). In Section 3.2 we describe the return type of RecogniseGroup (3.1-5) which we call recognition nodes. The methods to find homomorphisms are described in Section 3.3. Finally, we have three sections in which we collect conventions for the recognition of different types of groups.

3.1 The recursive procedure

-

At the heart of the recognition procedure is a function called RecogniseGeneric (3.1-1) which gets a GAP group object and returns a so-called "recognition node" (see Subsection 3.2 for details). Success or failure will be indicated by this record being in the filter IsReady (3.2-5) or not.

+

At the heart of the recognition procedure is a function called RecogniseGeneric (3.1-1) which gets a GAP group object and returns a so-called recognition node (see Subsection 3.2 for details). Success or failure will be indicated by this record being in the filter IsReady (3.2-5) or not.

To know how to find homomorphisms the function gets as another argument a database of methods (see Section 3.3 for a description of the setup for methods for finding homomorphisms and Section 4.1 in Chapter 4 for details about method databases). This database will be different according to the type of group in question.

@@ -233,7 +233,7 @@
3.2-1 RecogNodeFamily
3.2-2 IsRecogNode
‣ IsRecogNode( category )
-

and is IsAttributeStoringRep (Reference: IsAttributeStoringRep), such that we can define attributes for it, the values of which are stored once they are known. A recognition node always represents a whole binary tree of such records, see the attributes ImageRecogNode (3.2-10) and KernelRecogNode (3.2-11) below.

+

and is IsAttributeStoringRep (Reference: IsAttributeStoringRep), such that we can define attributes for it, the values of which are stored once they are known. A recognition node always represents a whole binary tree of such records, see the attributes ImageRecogNode (3.2-10) and KernelRecogNode (3.2-11) below.

Recognition nodes can be created via:

@@ -304,14 +304,14 @@
3.2-9 pregensfac
3.2-10 ImageRecogNode
‣ ImageRecogNode( ri )( attribute )
-

The value of this attribute is the recognition node of the image of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree. This attribute value provides the link to the "image" subtree of the recognition tree.

+

The value of this attribute is the recognition node of the image of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree. This attribute value provides the link to the image subtree of the recognition tree.

3.2-11 KernelRecogNode
‣ KernelRecogNode( ri )( attribute )
-

The value of this attribute is the recognition node of the kernel of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree or if the homomorphism is known to be an isomorphism. In the latter case the value of the attribute is set to fail. This attribute value provides the link to the "kernel" subtree of the recognition tree.

+

The value of this attribute is the recognition node of the kernel of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree or if the homomorphism is known to be an isomorphism. In the latter case the value of the attribute is set to fail. This attribute value provides the link to the kernel subtree of the recognition tree.

@@ -481,7 +481,7 @@
3.2-30 gensNslp
3.2-31 immediateverification
‣ immediateverification( ri )( attribute )
-

Sometimes a find homomorphism has information that it will be difficult to create generators for the kernel, for example if it is known that the kernel will need lots of generators. In that case this attribute with the default boolean value false can be set to true. In that case, the generic recursive recognition function will perform an immediate verification phase after the kernel has been recognised. This is done as follows: A few random elements are created, mapped through the homomorphism and written as an SLP in the nice generators there. Then this SLP is executed with preimages of those nice generators. The quotient lies then in the kernel and is written as an SLP in terms of the nice generators of the would be kernel. If this is not possible, then probably the creation of kernel generators was not complete and a few more kernel elements are produced and recognition in the kernel starts all over again. This is for example done in case of the "Imprimitive" method which maps onto the action on a block system. In that case, the kernel often needs lots of generators.

+

Sometimes a find homomorphism has information that it will be difficult to create generators for the kernel, for example if it is known that the kernel will need lots of generators. In that case this attribute with the default boolean value false can be set to true. In that case, the generic recursive recognition function will perform an immediate verification phase after the kernel has been recognised. This is done as follows: A few random elements are created, mapped through the homomorphism and written as an SLP in the nice generators there. Then this SLP is executed with preimages of those nice generators. The quotient lies then in the kernel and is written as an SLP in terms of the nice generators of the would be kernel. If this is not possible, then probably the creation of kernel generators was not complete and a few more kernel elements are produced and recognition in the kernel starts all over again. This is for example done in case of the Imprimitive method which maps onto the action on a block system. In that case, the kernel often needs lots of generators.

The following attributes are used to give a successful find homomorphism method further possibilities to transport knowledge about the group recognised by the current recognition node to the image or kernel of the found homomorphism:

@@ -504,21 +504,21 @@
3.2-33 InitialDataForImageRecogNode
3.2-34 isone
‣ isone( ri )( attribute )
-

This attribute returns a function that tests, whether or not an element of the group is equal to the identity or not. Usually this is just the operation IsOne (Reference: IsOne) but for projective groups it is a special function returning true for scalar matrices. In generic code, one should always use the result of this attribute to compare an element to the identity such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that tests, whether or not an element of the group is equal to the identity or not. Usually this is just the operation IsOne (Reference: IsOne) but for projective groups it is a special function returning true for scalar matrices. In generic code, one should always use the result of this attribute to compare an element to the identity such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

3.2-35 isequal
‣ isequal( ri )( attribute )
-

This attribute returns a function that compares two elements of the group being recognised. Usually this is just the operation EQ (Reference: equality of records) but for projective groups it is a special function checking for equality up to a scalar factor. In generic code, one should always use the result of this attribute to compare two elements such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that compares two elements of the group being recognised. Usually this is just the operation EQ (Reference: equality of records) but for projective groups it is a special function checking for equality up to a scalar factor. In generic code, one should always use the result of this attribute to compare two elements such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

3.2-36 OrderFunc
‣ OrderFunc( ri )( attribute )
-

This attribute returns a function that computes the order of an element of the group being recognised. Usually this is just the operation Order (Reference: Order) but for projective groups it is a special function. In generic code, one should always use the result of this attribute to compute the order of an element such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that computes the order of an element of the group being recognised. Usually this is just the operation Order (Reference: Order) but for projective groups it is a special function. In generic code, one should always use the result of this attribute to compute the order of an element such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

@@ -537,7 +537,7 @@
3.2-37 Other components of recognition nodes3.3 Methods to find homomorphisms
-

A "find homomorphism method" has the objective to, given a group G, either find a homomorphism from G onto a group, or to find an isomorphism, or to solve the constructive membership problem directly for G, or to fail.

+

A find homomorphism method has the objective to, given a group G, either find a homomorphism from G onto a group, or to find an isomorphism, or to solve the constructive membership problem directly for G, or to fail.

In case a homomorphism is found, it has to report that homomorphism back to the calling recursive recognition function together with as much information about the kernel as possible.

@@ -597,7 +597,7 @@
3.3-1 FindHomomorphism
-

To explain the calling conventions for SLPforElement (3.2-15) functions and for the sake of completeness we present now the function SLPforElementGeneric (3.3-2) which is used for the case of a "homomorphism node":

+

To explain the calling conventions for SLPforElement (3.2-15) functions and for the sake of completeness we present now the function SLPforElementGeneric (3.3-2) which is used for the case of a homomorphism node:

@@ -619,6 +619,6 @@
3.3-2 SLPforElementGeneric
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 Bib Ind
-

generated by GAPDoc2HTML

+

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diff --git a/doc/chap3_mj.html b/doc/chap3_mj.html index 0b6b8dd8..0082c3fd 100644 --- a/doc/chap3_mj.html +++ b/doc/chap3_mj.html @@ -6,7 +6,7 @@ GAP (recog) - Chapter 3: Group recognition @@ -91,15 +91,15 @@

3 Group recognition

The generic framework was designed having three situations in mind: permutation groups, matrix groups and projective groups. Although the methods used are quite different for those cases, there is a common pattern in the procedure of recognition. Namely, first we have to find a homomorphism, solve the constructive membership problem recursively in image and kernel, then put it together. The recursion ends in groups where we can solve the constructive membership problem directly. The general framework reflects this idea and separates it from the rest of the recognition methods.

-

Solution of the constructive membership problem comes in two stages: first a "recognition phase" and then a "verification phase". The recognition phase usually consists of randomised algorithms with certain error or failure probabilities. The result is some kind of "recognition information" that will describe the group already very well, but which is not yet proven to be correct. However, one can already write arbitrary elements in the group as product of the given generators. In the verification phase a presentation of the group is calculated, thereby proving that the group generated by the given generators is in fact isomorphic to the group described by the recognition information. In many cases the verification phase will be much more expensive than the recognition phase.

+

Solution of the constructive membership problem comes in two stages: first a recognition phase and then a verification phase. The recognition phase usually consists of randomised algorithms with certain error or failure probabilities. The result is some kind of recognition information that will describe the group already very well, but which is not yet proven to be correct. However, one can already write arbitrary elements in the group as product of the given generators. In the verification phase a presentation of the group is calculated, thereby proving that the group generated by the given generators is in fact isomorphic to the group described by the recognition information. In many cases the verification phase will be much more expensive than the recognition phase.

-

In the following sections, we describe the generic framework. We begin in Section 3.1 with a technical description of the recursive procedure behind our main function RecogniseGroup (3.1-5). In Section 3.2 we describe the return type of RecogniseGroup (3.1-5) which we call "recognition nodes". The methods to find homomorphisms are described in Section 3.3. Finally, we have three sections in which we collect conventions for the recognition of different types of groups.

+

In the following sections, we describe the generic framework. We begin in Section 3.1 with a technical description of the recursive procedure behind our main function RecogniseGroup (3.1-5). In Section 3.2 we describe the return type of RecogniseGroup (3.1-5) which we call recognition nodes. The methods to find homomorphisms are described in Section 3.3. Finally, we have three sections in which we collect conventions for the recognition of different types of groups.

3.1 The recursive procedure

-

At the heart of the recognition procedure is a function called RecogniseGeneric (3.1-1) which gets a GAP group object and returns a so-called "recognition node" (see Subsection 3.2 for details). Success or failure will be indicated by this record being in the filter IsReady (3.2-5) or not.

+

At the heart of the recognition procedure is a function called RecogniseGeneric (3.1-1) which gets a GAP group object and returns a so-called recognition node (see Subsection 3.2 for details). Success or failure will be indicated by this record being in the filter IsReady (3.2-5) or not.

To know how to find homomorphisms the function gets as another argument a database of methods (see Section 3.3 for a description of the setup for methods for finding homomorphisms and Section 4.1 in Chapter 4 for details about method databases). This database will be different according to the type of group in question.

@@ -236,7 +236,7 @@
3.2-1 RecogNodeFamily
3.2-2 IsRecogNode
‣ IsRecogNode( category )
-

and is IsAttributeStoringRep (Reference: IsAttributeStoringRep), such that we can define attributes for it, the values of which are stored once they are known. A recognition node always represents a whole binary tree of such records, see the attributes ImageRecogNode (3.2-10) and KernelRecogNode (3.2-11) below.

+

and is IsAttributeStoringRep (Reference: IsAttributeStoringRep), such that we can define attributes for it, the values of which are stored once they are known. A recognition node always represents a whole binary tree of such records, see the attributes ImageRecogNode (3.2-10) and KernelRecogNode (3.2-11) below.

Recognition nodes can be created via:

@@ -307,14 +307,14 @@
3.2-9 pregensfac
3.2-10 ImageRecogNode
‣ ImageRecogNode( ri )( attribute )
-

The value of this attribute is the recognition node of the image of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree. This attribute value provides the link to the "image" subtree of the recognition tree.

+

The value of this attribute is the recognition node of the image of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree. This attribute value provides the link to the image subtree of the recognition tree.

3.2-11 KernelRecogNode
‣ KernelRecogNode( ri )( attribute )
-

The value of this attribute is the recognition node of the kernel of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree or if the homomorphism is known to be an isomorphism. In the latter case the value of the attribute is set to fail. This attribute value provides the link to the "kernel" subtree of the recognition tree.

+

The value of this attribute is the recognition node of the kernel of the homomorphism that was found from the group described by the recognition node ri. It is set by the generic recursive procedure after a find homomorphism method has succeeded to find a homomorphism (or isomorphism). It does not have to be set in leaf nodes of the recognition tree or if the homomorphism is known to be an isomorphism. In the latter case the value of the attribute is set to fail. This attribute value provides the link to the kernel subtree of the recognition tree.

@@ -484,7 +484,7 @@
3.2-30 gensNslp
3.2-31 immediateverification
‣ immediateverification( ri )( attribute )
-

Sometimes a find homomorphism has information that it will be difficult to create generators for the kernel, for example if it is known that the kernel will need lots of generators. In that case this attribute with the default boolean value false can be set to true. In that case, the generic recursive recognition function will perform an immediate verification phase after the kernel has been recognised. This is done as follows: A few random elements are created, mapped through the homomorphism and written as an SLP in the nice generators there. Then this SLP is executed with preimages of those nice generators. The quotient lies then in the kernel and is written as an SLP in terms of the nice generators of the would be kernel. If this is not possible, then probably the creation of kernel generators was not complete and a few more kernel elements are produced and recognition in the kernel starts all over again. This is for example done in case of the "Imprimitive" method which maps onto the action on a block system. In that case, the kernel often needs lots of generators.

+

Sometimes a find homomorphism has information that it will be difficult to create generators for the kernel, for example if it is known that the kernel will need lots of generators. In that case this attribute with the default boolean value false can be set to true. In that case, the generic recursive recognition function will perform an immediate verification phase after the kernel has been recognised. This is done as follows: A few random elements are created, mapped through the homomorphism and written as an SLP in the nice generators there. Then this SLP is executed with preimages of those nice generators. The quotient lies then in the kernel and is written as an SLP in terms of the nice generators of the would be kernel. If this is not possible, then probably the creation of kernel generators was not complete and a few more kernel elements are produced and recognition in the kernel starts all over again. This is for example done in case of the Imprimitive method which maps onto the action on a block system. In that case, the kernel often needs lots of generators.

The following attributes are used to give a successful find homomorphism method further possibilities to transport knowledge about the group recognised by the current recognition node to the image or kernel of the found homomorphism:

@@ -507,21 +507,21 @@
3.2-33 InitialDataForImageRecogNode
3.2-34 isone
‣ isone( ri )( attribute )
-

This attribute returns a function that tests, whether or not an element of the group is equal to the identity or not. Usually this is just the operation IsOne (Reference: IsOne) but for projective groups it is a special function returning true for scalar matrices. In generic code, one should always use the result of this attribute to compare an element to the identity such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that tests, whether or not an element of the group is equal to the identity or not. Usually this is just the operation IsOne (Reference: IsOne) but for projective groups it is a special function returning true for scalar matrices. In generic code, one should always use the result of this attribute to compare an element to the identity such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

3.2-35 isequal
‣ isequal( ri )( attribute )
-

This attribute returns a function that compares two elements of the group being recognised. Usually this is just the operation EQ (Reference: equality of records) but for projective groups it is a special function checking for equality up to a scalar factor. In generic code, one should always use the result of this attribute to compare two elements such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that compares two elements of the group being recognised. Usually this is just the operation EQ (Reference: equality of records) but for projective groups it is a special function checking for equality up to a scalar factor. In generic code, one should always use the result of this attribute to compare two elements such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

3.2-36 OrderFunc
‣ OrderFunc( ri )( attribute )
-

This attribute returns a function that computes the order of an element of the group being recognised. Usually this is just the operation Order (Reference: Order) but for projective groups it is a special function. In generic code, one should always use the result of this attribute to compute the order of an element such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

+

This attribute returns a function that computes the order of an element of the group being recognised. Usually this is just the operation Order (Reference: Order) but for projective groups it is a special function. In generic code, one should always use the result of this attribute to compute the order of an element such that the code works also for projective groups. Find homomorphism methods usually do not have to set this attribute.

@@ -540,7 +540,7 @@
3.2-37 Other components of recognition nodes3.3 Methods to find homomorphisms
-

A "find homomorphism method" has the objective to, given a group \(G\), either find a homomorphism from \(G\) onto a group, or to find an isomorphism, or to solve the constructive membership problem directly for \(G\), or to fail.

+

A find homomorphism method has the objective to, given a group \(G\), either find a homomorphism from \(G\) onto a group, or to find an isomorphism, or to solve the constructive membership problem directly for \(G\), or to fail.

In case a homomorphism is found, it has to report that homomorphism back to the calling recursive recognition function together with as much information about the kernel as possible.

@@ -600,7 +600,7 @@
3.3-1 FindHomomorphism
-

To explain the calling conventions for SLPforElement (3.2-15) functions and for the sake of completeness we present now the function SLPforElementGeneric (3.3-2) which is used for the case of a "homomorphism node":

+

To explain the calling conventions for SLPforElement (3.2-15) functions and for the sake of completeness we present now the function SLPforElementGeneric (3.3-2) which is used for the case of a homomorphism node:

@@ -622,6 +622,6 @@
3.3-2 SLPforElementGeneric
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diff --git a/doc/chap4.html b/doc/chap4.html index 7c9d3a06..3ccc8675 100644 --- a/doc/chap4.html +++ b/doc/chap4.html @@ -65,9 +65,9 @@

4 Method selection

The design is intentionally kept as simple as possible and at the same time as versatile as possible, thereby providing a useful framework for many situations as described above.

-

Note the differences to the GAP method selection, which is designed with the idea in mind that it will be quite clear in most situations, which one is "the best" method for a given set of input data, and that we do not want to try different things. On the other hand, the GAP method selection is quite complicated, which is to some extend necessary to make sure, that lots of different information about the objects in question can be used to really find the best method.

+

Note the differences to the GAP method selection, which is designed with the idea in mind that it will be quite clear in most situations, which one is the best method for a given set of input data, and that we do not want to try different things. On the other hand, the GAP method selection is quite complicated, which is to some extend necessary to make sure, that lots of different information about the objects in question can be used to really find the best method.

-

Our setup here in particular has to fulfill the requirement, that in the end, with lots of methods installed, one still has to be able to have an overview and to "prove", that the whole system always does the right thing.

+

Our setup here in particular has to fulfill the requirement, that in the end, with lots of methods installed, one still has to be able to have an overview and to prove, that the whole system always does the right thing.

@@ -204,7 +204,7 @@
4.3-1 CallMethods

The argument db must be a method database in the sense of Section 4.2. limit must be a non-negative integer. furtherargs stands for an arbitrary number of additional arguments, which are handed down to the called methods. Of course they must fulfill the conventions defined for the methods in the database db.

-

The function first creates a "method selection" record keeping track of the things that happened during the method trying procedure, which is also used during this procedure. Then it calls methods with the algorithm described below and in the end returns the method selection record in its final state.

+

The function first creates a method selection record keeping track of the things that happened during the method trying procedure, which is also used during this procedure. Then it calls methods with the algorithm described below and in the end returns the method selection record in its final state.

The method selection record has the following components:

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4.4-8 SLPforElementFuncsGeneric
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4 Method selection

The design is intentionally kept as simple as possible and at the same time as versatile as possible, thereby providing a useful framework for many situations as described above.

-

Note the differences to the GAP method selection, which is designed with the idea in mind that it will be quite clear in most situations, which one is "the best" method for a given set of input data, and that we do not want to try different things. On the other hand, the GAP method selection is quite complicated, which is to some extend necessary to make sure, that lots of different information about the objects in question can be used to really find the best method.

+

Note the differences to the GAP method selection, which is designed with the idea in mind that it will be quite clear in most situations, which one is the best method for a given set of input data, and that we do not want to try different things. On the other hand, the GAP method selection is quite complicated, which is to some extend necessary to make sure, that lots of different information about the objects in question can be used to really find the best method.

-

Our setup here in particular has to fulfill the requirement, that in the end, with lots of methods installed, one still has to be able to have an overview and to "prove", that the whole system always does the right thing.

+

Our setup here in particular has to fulfill the requirement, that in the end, with lots of methods installed, one still has to be able to have an overview and to prove, that the whole system always does the right thing.

@@ -207,7 +207,7 @@
4.3-1 CallMethods

The argument db must be a method database in the sense of Section 4.2. limit must be a non-negative integer. furtherargs stands for an arbitrary number of additional arguments, which are handed down to the called methods. Of course they must fulfill the conventions defined for the methods in the database db.

-

The function first creates a "method selection" record keeping track of the things that happened during the method trying procedure, which is also used during this procedure. Then it calls methods with the algorithm described below and in the end returns the method selection record in its final state.

+

The function first creates a method selection record keeping track of the things that happened during the method trying procedure, which is also used during this procedure. Then it calls methods with the algorithm described below and in the end returns the method selection record in its final state.

The method selection record has the following components:

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4.4-8 SLPforElementFuncsGeneric
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5 After successful recognition

K:<recognition node Giant Size=479001600>> -

One sees that the recursive process runs, first it finds that the permutation action is not transitive, a homomorphism is found by mapping onto the action on one of the orbits. The image is recognised to permute only a few points. The kernel is recognised to be a full symmetric group in its natural action on at least 10 points (recognised as "Giant").

+

One sees that the recursive process runs, first it finds that the permutation action is not transitive, a homomorphism is found by mapping onto the action on one of the orbits. The image is recognised to permute only a few points. The kernel is recognised to be a full symmetric group in its natural action on at least 10 points (recognised as Giant).

After this, we can write arbitrary group elements in the group g in terms of the nice generators:

@@ -119,7 +119,7 @@
5.1-4 DisplayCompositionFactors
‣ DisplayCompositionFactors( ri )( function )

Returns: nothing

-

This function displays a composition series by using the recursive recognition tree. It only works, if the usual operation CompositionSeries (Reference: CompositionSeries) works for all leaves. THIS DOES CURRENTLY NOT WORK FOR PROJECTIVE GROUPS AND THUS FOR MATRIX GROUPS!

+

This function displays a composition series by using the recursive recognition tree. It only works, if the usual operation CompositionSeries (Reference: CompositionSeries) works for all leaves. THIS DOES CURRENTLY NOT WORK FOR PROJECTIVE GROUPS AND THUS FOR MATRIX GROUPS!

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
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5.1-4 DisplayCompositionFactors
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5 After successful recognition

K:<recognition node Giant Size=479001600>> -

One sees that the recursive process runs, first it finds that the permutation action is not transitive, a homomorphism is found by mapping onto the action on one of the orbits. The image is recognised to permute only a few points. The kernel is recognised to be a full symmetric group in its natural action on at least 10 points (recognised as "Giant").

+

One sees that the recursive process runs, first it finds that the permutation action is not transitive, a homomorphism is found by mapping onto the action on one of the orbits. The image is recognised to permute only a few points. The kernel is recognised to be a full symmetric group in its natural action on at least 10 points (recognised as Giant).

After this, we can write arbitrary group elements in the group g in terms of the nice generators:

@@ -122,7 +122,7 @@
5.1-4 DisplayCompositionFactors
‣ DisplayCompositionFactors( ri )( function )

Returns: nothing

-

This function displays a composition series by using the recursive recognition tree. It only works, if the usual operation CompositionSeries (Reference: CompositionSeries) works for all leaves. THIS DOES CURRENTLY NOT WORK FOR PROJECTIVE GROUPS AND THUS FOR MATRIX GROUPS!

+

This function displays a composition series by using the recursive recognition tree. It only works, if the usual operation CompositionSeries (Reference: CompositionSeries) works for all leaves. THIS DOES CURRENTLY NOT WORK FOR PROJECTIVE GROUPS AND THUS FOR MATRIX GROUPS!

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
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5.1-4 DisplayCompositionFactors
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6.4-1 AltSymBBByDegreeThis method is a black box constructive (?) recognition of alternating and symmetric groups.

-

This algorithm is probably based on the paper [BLGN+05].

+

This algorithm is probably based on the paper [BLN+05].

@@ -764,7 +764,7 @@
6.4-17 LowIndex

This method is used for recognizing projective groups.

-

This method is designed for the handling of the Aschbacher class C2 (stabiliser of a decomposition of the underlying vector space), but may succeed on other types of input as well. Given G ≤ PGL(d,q), the output is either the permutation action of G on a short orbit of subspaces or fail. In the current setup, "short orbit" is defined to have length at most 4d.

+

This method is designed for the handling of the Aschbacher class C2 (stabiliser of a decomposition of the underlying vector space), but may succeed on other types of input as well. Given G ≤ PGL(d,q), the output is either the permutation action of G on a short orbit of subspaces or fail. In the current setup, short orbit is defined to have length at most 4d.

@@ -830,7 +830,7 @@
6.4-25 TensorDecomposableTODO/FIXME: it is unclear if the following description actually belongs to this method, so be cautious!

-

This method currently tries to find one tensor factor by powering up commutators of random elements to elements of prime order. This seems to work quite well provided that the two tensor factors are not "linked" too much such that there exist enough elements that act with different orders on both tensor factors.

+

This method currently tries to find one tensor factor by powering up commutators of random elements to elements of prime order. This seems to work quite well provided that the two tensor factors are not linked too much such that there exist enough elements that act with different orders on both tensor factors.

This method and its description needs some improvement.

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6.5 Unused methods

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6.4-1 AltSymBBByDegreeThis method is a black box constructive (?) recognition of alternating and symmetric groups.

-

This algorithm is probably based on the paper [BLGN+05].

+

This algorithm is probably based on the paper [BLN+05].

@@ -767,7 +767,7 @@
6.4-17 LowIndex

This method is used for recognizing projective groups.

-

This method is designed for the handling of the Aschbacher class C2 (stabiliser of a decomposition of the underlying vector space), but may succeed on other types of input as well. Given G \( \le PGL(d,q)\), the output is either the permutation action of G on a short orbit of subspaces or fail. In the current setup, "short orbit" is defined to have length at most \(4d\).

+

This method is designed for the handling of the Aschbacher class C2 (stabiliser of a decomposition of the underlying vector space), but may succeed on other types of input as well. Given G \( \le PGL(d,q)\), the output is either the permutation action of G on a short orbit of subspaces or fail. In the current setup, short orbit is defined to have length at most \(4d\).

@@ -833,7 +833,7 @@
6.4-25 TensorDecomposableTODO/FIXME: it is unclear if the following description actually belongs to this method, so be cautious!

-

This method currently tries to find one tensor factor by powering up commutators of random elements to elements of prime order. This seems to work quite well provided that the two tensor factors are not "linked" too much such that there exist enough elements that act with different orders on both tensor factors.

+

This method currently tries to find one tensor factor by powering up commutators of random elements to elements of prime order. This seems to work quite well provided that the two tensor factors are not linked too much such that there exist enough elements that act with different orders on both tensor factors.

This method and its description needs some improvement.

@@ -967,6 +967,6 @@

6.5 Unused methods

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7 Examples

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7 Examples

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8 Renaming

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8 Renaming

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9.3 Splitting methods

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9.3 Splitting methods

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References

-[AB01] Altseimer, C. and Borovik, A. V., +[AB01] Altseimer, C. and Borovik, A. V., Probabilistic recognition of orthogonal and symplectic groups, in Groups and computation, III (Columbus, OH, 1999), @@ -40,7 +40,7 @@

References

-[BB99] Babai, L. and Beals, R., +[BB99] Babai, L. and Beals, R., A polynomial-time theory of black box groups. I, in Groups St. Andrews 1997 in Bath, I, @@ -54,7 +54,7 @@

References

-[BBS09] Babai, L., Beals, R. and Seress, Á., +[BBS09] Babai, L., Beals, R. and Seress, Á., Polynomial-time theory of matrix groups, in STOC'09–-Proceedings of the 2009 ACM International @@ -67,7 +67,7 @@

References

-[BHLGO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., +[BHLO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., A practical model for computation with matrix groups, J. Symbolic Comput., 68 (part 1) @@ -79,7 +79,7 @@

References

-[BK01] Brooksbank, P. A. and Kantor, W. M., +[BK01] Brooksbank, P. A. and Kantor, W. M., On constructive recognition of a black box PSL(d,q), in Groups and computation, III (Columbus, OH, 1999), @@ -93,7 +93,7 @@

References

-[BK06] Brooksbank, P. A. and Kantor, W. M., +[BK06] Brooksbank, P. A. and Kantor, W. M., Fast constructive recognition of black box orthogonal groups, J. Algebra, 300 (1) @@ -105,7 +105,7 @@

References

-[BKPS02] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á., +[BKPS02] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á., Black-box recognition of finite simple groups of Lie type by statistics of element orders, J. Group Theory, @@ -118,7 +118,7 @@

References

-[BLGN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., +[BLN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., A black-box group algorithm for recognizing finite symmetric and alternating groups. I, Trans. Amer. Math. Soc., @@ -131,7 +131,7 @@

References

-[BLGN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., +[BLN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., Constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules, @@ -145,7 +145,7 @@

References

-[BLS97] Babai, L., Luks, E. M. and Seress, Á., +[BLS97] Babai, L., Luks, E. M. and Seress, Á., Fast management of permutation groups. I, SIAM J. Comput., 26 (5) @@ -157,7 +157,7 @@

References

-[BNS06] Brooksbank, P., Niemeyer, A. C. and Seress, Á., +[BNS06] Brooksbank, P., Niemeyer, A. C. and Seress, Á., A reduction algorithm for matrix groups with an extraspecial normal subgroup, in Finite geometries, groups, and computation, @@ -169,7 +169,7 @@

References

-[Bro01] Brooksbank, P. A., +[Bro01] Brooksbank, P. A., A constructive recognition algorithm for the matrix group Ω(d,q), in Groups and computation, III (Columbus, OH, @@ -184,7 +184,7 @@

References

-[Bro03] Brooksbank, P. A., +[Bro03] Brooksbank, P. A., Fast constructive recognition of black-box unitary groups, LMS J. Comput. Math., 6 @@ -196,7 +196,7 @@

References

-[Bro08] Brooksbank, P. A., +[Bro08] Brooksbank, P. A., Fast constructive recognition of black box symplectic groups, J. Algebra, 320 (2) @@ -208,7 +208,7 @@

References

-[BS01] Babai, L. and Shalev, A., +[BS01] Babai, L. and Shalev, A., Recognizing simplicity of black-box groups and the frequency of p-singular elements in affine groups, in Groups and computation, III (Columbus, OH, @@ -223,7 +223,7 @@

References

-[CFL97] Cooperman, G., Finkelstein, L. and Linton, S., +[CFL97] Cooperman, G., Finkelstein, L. and Linton, S., Constructive recognition of a black box group isomorphic to GL(n,2), in Groups and computation, II (New Brunswick, @@ -238,7 +238,7 @@

References

-[CLG97a] Celler, F. and Leedham-Green, C. R., +[CL97a] Celler, F. and Leedham-Green, C. R., Calculating the order of an invertible matrix, in Groups and computation, II (New Brunswick, NJ, 1995), @@ -252,7 +252,7 @@

References

-[CLG97b] Celler, F. and Leedham-Green, C. R., +[CL97b] Celler, F. and Leedham-Green, C. R., A non-constructive recognition algorithm for the special linear and other classical groups, in Groups and computation, II (New Brunswick, @@ -267,7 +267,7 @@

References

-[CLG98] Celler, F. and Leedham-Green, C. R., +[CL98] Celler, F. and Leedham-Green, C. R., A constructive recognition algorithm for the special linear group, in The atlas of finite groups: ten years on (Birmingham, @@ -283,7 +283,7 @@

References

-[CLG01] Conder, M. and Leedham-Green, C. R., +[CL01] Conder, M. and Leedham-Green, C. R., Fast recognition of classical groups over large fields, in Groups and computation, III (Columbus, OH, 1999), @@ -297,7 +297,7 @@

References

-[CLGM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A., +[CLM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A., Generating random elements of a finite group, Comm. Algebra, 23 (13) @@ -309,7 +309,7 @@

References

-[CLGO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., +[CLO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of PSL(2,q), Trans. Amer. Math. Soc., 358 (3) @@ -321,7 +321,7 @@

References

-[CNRD09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., +[CNR09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., A polynomial-time reduction algorithm for groups of semilinear or subfield class, J. Algebra, @@ -334,7 +334,7 @@

References

-[DLGLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., +[DLLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., Constructive recognition of classical groups in even characteristic, J. Algebra, @@ -347,7 +347,7 @@

References

-[DLGO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., +[DLO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., Effective black-box constructive recognition of classical groups, J. Algebra, @@ -360,7 +360,7 @@

References

-[GH97] Glasby, S. P. and Howlett, R. B., +[GH97] Glasby, S. P. and Howlett, R. B., Writing representations over minimal fields, Comm. Algebra, 25 (6) @@ -372,7 +372,7 @@

References

-[GLGO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., +[GLO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., Writing projective representations over subfields, J. Algebra, 295 (1) @@ -382,9 +382,21 @@

References

+

+

+[HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A., + Constructive membership in black-box groups, + J. Group Theory, + 11 (6) + (2008), + 747–763
+(https://doi.org/10.1515/JGT.2008.047). +

+ +

-[HLGOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., +[HLOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Computing matrix group decompositions with respect to a normal subgroup, J. Algebra, @@ -397,7 +409,7 @@

References

-[HLGOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., +[HLOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Testing matrix groups for primitivity, J. Algebra, 184 (3) @@ -407,21 +419,9 @@

References

-

-

-[HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A., - Constructive membership in black-box groups, - J. Group Theory, - 11 (6) - (2008), - 747–763
-(https://doi.org/10.1515/JGT.2008.047). -

- -

-[HR94] Holt, D. F. and Rees, S., +[HR94] Holt, D. F. and Rees, S., Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57 (1) @@ -432,7 +432,7 @@

References

-[IL00] Ivanyos, G. and Lux, K., +[IL00] Ivanyos, G. and Lux, K., Treating the exceptional cases of the MeatAxe, Experiment. Math., 9 (3) @@ -444,7 +444,7 @@

References

-[JLNP13] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W., +[JLNP13] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W., Fast recognition of alternating groups of unknown degree, J. Algebra, 392 @@ -456,7 +456,7 @@

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-[KK15] Kantor, W. M. and Kassabov, M., +[KK15] Kantor, W. M. and Kassabov, M., Black box groups isomorphic to PGL(2,2^e), J. Algebra, 421 @@ -468,7 +468,7 @@

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-[KM13] Kantor, W. M. and Magaard, K., +[KM13] Kantor, W. M. and Magaard, K., Black box exceptional groups of Lie type, Trans. Amer. Math. Soc., 365 (9) @@ -480,7 +480,7 @@

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-[KM15] Kantor, W. M. and Magaard, K., +[KM15] Kantor, W. M. and Magaard, K., Black box exceptional groups of Lie type II, J. Algebra, 421 @@ -492,7 +492,7 @@

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-[KS09] Kantor, W. M. and Seress, Á., +[KS09] Kantor, W. M. and Seress, Á., Large element orders and the characteristic of Lie-type simple groups, J. Algebra, @@ -505,7 +505,7 @@

References

-[LG01] Leedham-Green, C. R., +[Lee01] Leedham-Green, C. R., The computational matrix group project, in Groups and computation, III (Columbus, OH, 1999), @@ -517,9 +517,34 @@

References

+

+

+[LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A., + Constructive recognition of SL_3(q), + J. Algebra, + 316 (2) + (2007), + 619–633
+(https://doi.org/10.1016/j.jalgebra.2007.01.020). +

+ + +

+

+[LNPS06] Law, M., Niemeyer, A. C., Praeger, C. E. and Seress, Á., + A reduction algorithm for large-base primitive permutation + groups, + LMS J. Comput. Math., + 9 + (2006), + 159–173
+(https://doi.org/10.1112/S1461157000001236). +

+ +

-[LGO97a] Leedham-Green, C. R. and O'Brien, E. A., +[LO97a] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor products of matrix groups, Internat. J. Algebra Comput., 7 (5) @@ -531,7 +556,7 @@

References

-[LGO97b] Leedham-Green, C. R. and O'Brien, E. A., +[LO97b] Leedham-Green, C. R. and O'Brien, E. A., Tensor products are projective geometries, J. Algebra, 189 (2) @@ -543,7 +568,7 @@

References

-[LGO02] Leedham-Green, C. R. and O'Brien, E. A., +[LO02] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor-induced matrix groups, J. Algebra, 253 (1) @@ -553,9 +578,21 @@

References

+

+

+[LO07] Liebeck, M. W. and O'Brien, E. A., + Finding the characteristic of a group of Lie type, + J. Lond. Math. Soc. (2), + 75 (3) + (2007), + 741–754
+(https://doi.org/10.1112/jlms/jdm028). +

+ +

-[LGO09] Leedham-Green, C. R. and O'Brien, E. A., +[LO09] Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of classical groups in odd characteristic, J. Algebra, @@ -566,46 +603,9 @@

References

-

-

-[LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A., - Constructive recognition of SL_3(q), - J. Algebra, - 316 (2) - (2007), - 619–633
-(https://doi.org/10.1016/j.jalgebra.2007.01.020). -

- - -

-

-[LNPS06] Law, M., Niemeyer, A. C., Praeger, C. E. and Seress, Á., - A reduction algorithm for large-base primitive permutation - groups, - LMS J. Comput. Math., - 9 - (2006), - 159–173
-(https://doi.org/10.1112/S1461157000001236). -

- - -

-

-[LO07] Liebeck, M. W. and O'Brien, E. A., - Finding the characteristic of a group of Lie type, - J. Lond. Math. Soc. (2), - 75 (3) - (2007), - 741–754
-(https://doi.org/10.1112/jlms/jdm028). -

- -

-[LO16] Liebeck, M. W. and O'Brien, E. A., +[LO16] Liebeck, M. W. and O'Brien, E. A., Recognition of finite exceptional groups of Lie type, Trans. Amer. Math. Soc., 368 (9) @@ -628,7 +628,7 @@

References

-[Nie05] Niemeyer, A. C., +[Nie05] Niemeyer, A. C., Constructive recognition of normalizers of small extra-special matrix groups, Internat. J. Algebra Comput., @@ -641,7 +641,7 @@

References

-[NP92] Neumann, P. M. and Praeger, C. E., +[NP92] Neumann, P. M. and Praeger, C. E., A recognition algorithm for special linear groups, Proc. London Math. Soc. (3), 65 (3) @@ -653,7 +653,7 @@

References

-[NP97] Niemeyer, A. C. and Praeger, C. E., +[NP97] Niemeyer, A. C. and Praeger, C. E., Implementing a recognition algorithm for classical groups, in Groups and computation, II (New Brunswick, NJ, 1995), @@ -667,7 +667,7 @@

References

-[NP98] Niemeyer, A. C. and Praeger, C. E., +[NP98] Niemeyer, A. C. and Praeger, C. E., A recognition algorithm for classical groups over finite fields, Proc. London Math. Soc. (3), @@ -680,7 +680,7 @@

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-[NP99] Niemeyer, A. C. and Praeger, C. E., +[NP99] Niemeyer, A. C. and Praeger, C. E., A recognition algorithm for non-generic classical groups over finite fields, J. Austral. Math. Soc. Ser. A, @@ -692,7 +692,7 @@

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-[NS06] Neunhöffer, M. and Seress, Á., +[NS06] Neunhöffer, M. and Seress, Á., A data structure for a uniform approach to computations with finite groups, in ISSAC 2006, @@ -706,7 +706,7 @@

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-[O'B06] O'Brien, E. A., +[O'B06] O'Brien, E. A., Towards effective algorithms for linear groups, in Finite geometries, groups, and computation, Walter de Gruyter, Berlin @@ -717,7 +717,7 @@

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-[O'B11] O'Brien, E. A., +[O'B11] O'Brien, E. A., Algorithms for matrix groups, in Groups St Andrews 2009 in Bath. Volume 2, @@ -731,7 +731,7 @@

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-[Pak00] Pak, I., +[Pak00] Pak, I., The product replacement algorithm is polynomial, in 41st Annual Symposium on Foundations of Computer @@ -745,7 +745,7 @@

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-[Par84] Parker, R. A., +[Par84] Parker, R. A., The computer calculation of modular characters (the meat-axe), in Computational group theory (Durham, 1982), Academic Press, London @@ -756,7 +756,7 @@

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-[Pra99] Praeger, C. E., +[Pra99] Praeger, C. E., Primitive prime divisor elements in finite classical groups, in Groups St. Andrews 1997 in Bath, II, @@ -771,7 +771,7 @@

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-[Ser03] Seress, Á., +[Ser03] Seress, Á., Permutation group algorithms, Cambridge University Press, Cambridge, Cambridge Tracts in Mathematics, @@ -790,6 +790,6 @@

References

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diff --git a/doc/chapBib.txt b/doc/chapBib.txt index 9a8f328a..d9d92c48 100644 --- a/doc/chapBib.txt +++ b/doc/chapBib.txt @@ -14,7 +14,7 @@ matrix groups, in STOC'09–-Proceedings of the 2009 ACM International Symposium on Theory of Computing, ACM, New York (2009), 55–64. - [BHLGO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., + [BHLO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., A practical model for computation with matrix groups, J. Symbolic Comput., 68, part 1 (2015), 27–60, (https://doi.org/10.1016/j.jsc.2014.08.006). @@ -31,12 +31,12 @@ orders, J. Group Theory, 5, 4 (2002), 383–401, (https://doi.org/10.1515/jgth.2002.010). - [BLGN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. + [BLN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., A black-box group algorithm for recognizing finite symmetric and alternating groups. I, Trans. Amer. Math. Soc., 355, 5 (2003), 2097–2113, (https://doi.org/10.1090/S0002-9947-03-03040-X). - [BLGN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. + [BLN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., Constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules, J. Algebra, 292, 1 (2005), 4–46, @@ -72,47 +72,47 @@ computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28 (1997), 85–100. - [CLG97a] Celler, F. and Leedham-Green, C. R., Calculating the order of an + [CL97a] Celler, F. and Leedham-Green, C. R., Calculating the order of an invertible matrix, in Groups and computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28 (1997), 55–60. - [CLG97b] Celler, F. and Leedham-Green, C. R., A non-constructive recognition + [CL97b] Celler, F. and Leedham-Green, C. R., A non-constructive recognition algorithm for the special linear and other classical groups, in Groups and computation, II (New Brunswick, NJ, 1995), Amer. Math. Soc., Providence, RI, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 28 (1997), 61–67. - [CLG98] Celler, F. and Leedham-Green, C. R., A constructive recognition + [CL98] Celler, F. and Leedham-Green, C. R., A constructive recognition algorithm for the special linear group, in The atlas of finite groups: ten years on (Birmingham, 1995), Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 249 (1998), 11–26, (https://doi.org/10.1017/CBO9780511565830.007). - [CLG01] Conder, M. and Leedham-Green, C. R., Fast recognition of classical + [CL01] Conder, M. and Leedham-Green, C. R., Fast recognition of classical groups over large fields, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 113–121. - [CLGM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. + [CLM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A., Generating random elements of a finite group, Comm. Algebra, 23, 13 (1995), 4931–4948, (https://doi.org/10.1080/00927879508825509). - [CLGO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., + [CLO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of PSL(2,q), Trans. Amer. Math. Soc., 358, 3 (2006), 1203–1221, (https://doi.org/10.1090/S0002-9947-05-03756-6). - [CNRD09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., A + [CNR09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., A polynomial-time reduction algorithm for groups of semilinear or subfield class, J. Algebra, 322, 3 (2009), 613–637, (https://doi.org/10.1016/j.jalgebra.2009.04.022). - [DLGLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., + [DLLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., Constructive recognition of classical groups in even characteristic, J. Algebra, 391 (2013), 227–255, (https://doi.org/10.1016/j.jalgebra.2013.04.031). - [DLGO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., Effective + [DLO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., Effective black-box constructive recognition of classical groups, J. Algebra, 421 (2015), 460–492, (https://doi.org/10.1016/j.jalgebra.2014.08.039). @@ -120,22 +120,22 @@ minimal fields, Comm. Algebra, 25, 6 (1997), 1703–1711, (https://doi.org/10.1080/00927879708825947). - [GLGO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., Writing + [GLO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., Writing projective representations over subfields, J. Algebra, 295, 1 (2006), 51–61, (https://doi.org/10.1016/j.jalgebra.2005.03.037). - [HLGOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., + [HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and + Wilson, R. A., Constructive membership in black-box groups, J. Group Theory, + 11, 6 (2008), 747–763, (https://doi.org/10.1515/JGT.2008.047). + + [HLOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Computing matrix group decompositions with respect to a normal subgroup, J. Algebra, 184, 3 (1996), 818–838, (https://doi.org/10.1006/jabr.1996.0286). - [HLGOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., + [HLOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Testing matrix groups for primitivity, J. Algebra, 184, 3 (1996), 795–817, (https://doi.org/10.1006/jabr.1996.0285). - [HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and - Wilson, R. A., Constructive membership in black-box groups, J. Group Theory, - 11, 6 (2008), 747–763, (https://doi.org/10.1515/JGT.2008.047). - [HR94] Holt, D. F. and Rees, S., Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57, 1 (1994), 1–16. @@ -163,26 +163,10 @@ characteristic of Lie-type simple groups, J. Algebra, 322, 3 (2009), 802–832, (https://doi.org/10.1016/j.jalgebra.2009.05.004). - [LG01] Leedham-Green, C. R., The computational matrix group project, in + [Lee01] Leedham-Green, C. R., The computational matrix group project, in Groups and computation, III (Columbus, OH, 1999), de Gruyter, Berlin, Ohio State Univ. Math. Res. Inst. Publ., 8 (2001), 229–247. - [LGO97a] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor - products of matrix groups, Internat. J. Algebra Comput., 7, 5 (1997), - 541–559, (https://doi.org/10.1142/S0218196797000241). - - [LGO97b] Leedham-Green, C. R. and O'Brien, E. A., Tensor products are - projective geometries, J. Algebra, 189, 2 (1997), 514–528, - (https://doi.org/10.1006/jabr.1996.6881). - - [LGO02] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor-induced - matrix groups, J. Algebra, 253, 1 (2002), 14–30, - (https://doi.org/10.1016/S0021-8693(02)00041-8). - - [LGO09] Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of - classical groups in odd characteristic, J. Algebra, 322, 3 (2009), 833–881, - (https://doi.org/10.1016/j.jalgebra.2009.04.028). - [LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A., Constructive recognition of SL_3(q), J. Algebra, 316, 2 (2007), 619–633, (https://doi.org/10.1016/j.jalgebra.2007.01.020). @@ -192,10 +176,26 @@ Comput. Math., 9 (2006), 159–173, (https://doi.org/10.1112/S1461157000001236). + [LO97a] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor products + of matrix groups, Internat. J. Algebra Comput., 7, 5 (1997), 541–559, + (https://doi.org/10.1142/S0218196797000241). + + [LO97b] Leedham-Green, C. R. and O'Brien, E. A., Tensor products are + projective geometries, J. Algebra, 189, 2 (1997), 514–528, + (https://doi.org/10.1006/jabr.1996.6881). + + [LO02] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor-induced + matrix groups, J. Algebra, 253, 1 (2002), 14–30, + (https://doi.org/10.1016/S0021-8693(02)00041-8). + [LO07] Liebeck, M. W. and O'Brien, E. A., Finding the characteristic of a group of Lie type, J. Lond. Math. Soc. (2), 75, 3 (2007), 741–754, (https://doi.org/10.1112/jlms/jdm028). + [LO09] Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of + classical groups in odd characteristic, J. Algebra, 322, 3 (2009), 833–881, + (https://doi.org/10.1016/j.jalgebra.2009.04.028). + [LO16] Liebeck, M. W. and O'Brien, E. A., Recognition of finite exceptional groups of Lie type, Trans. Amer. Math. Soc., 368, 9 (2016), 6189–6226, (https://doi.org/10.1090/tran/6534). diff --git a/doc/chapBib_mj.html b/doc/chapBib_mj.html index f4788ad5..6f2f7eda 100644 --- a/doc/chapBib_mj.html +++ b/doc/chapBib_mj.html @@ -6,7 +6,7 @@ GAP (recog) - References @@ -30,7 +30,7 @@

References

-[AB01] Altseimer, C. and Borovik, A. V., +[AB01] Altseimer, C. and Borovik, A. V., Probabilistic recognition of orthogonal and symplectic groups, in Groups and computation, III (Columbus, OH, 1999), @@ -43,7 +43,7 @@

References

-[BB99] Babai, L. and Beals, R., +[BB99] Babai, L. and Beals, R., A polynomial-time theory of black box groups. I, in Groups St. Andrews 1997 in Bath, I, @@ -57,7 +57,7 @@

References

-[BBS09] Babai, L., Beals, R. and Seress, Á., +[BBS09] Babai, L., Beals, R. and Seress, Á., Polynomial-time theory of matrix groups, in STOC'09–-Proceedings of the 2009 ACM International @@ -70,7 +70,7 @@

References

-[BHLGO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., +[BHLO15] Bäärnhielm, H., Holt, D., Leedham-Green, C. R. and O'Brien, E. A., A practical model for computation with matrix groups, J. Symbolic Comput., 68 (part 1) @@ -82,7 +82,7 @@

References

-[BK01] Brooksbank, P. A. and Kantor, W. M., +[BK01] Brooksbank, P. A. and Kantor, W. M., On constructive recognition of a black box \({\rm PSL}(d,q)\), in Groups and computation, III (Columbus, OH, @@ -97,7 +97,7 @@

References

-[BK06] Brooksbank, P. A. and Kantor, W. M., +[BK06] Brooksbank, P. A. and Kantor, W. M., Fast constructive recognition of black box orthogonal groups, J. Algebra, 300 (1) @@ -109,7 +109,7 @@

References

-[BKPS02] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á., +[BKPS02] Babai, L., Kantor, W. M., Pálfy, P. P. and Seress, Á., Black-box recognition of finite simple groups of Lie type by statistics of element orders, J. Group Theory, @@ -122,7 +122,7 @@

References

-[BLGN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., +[BLN+03] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., A black-box group algorithm for recognizing finite symmetric and alternating groups. I, Trans. Amer. Math. Soc., @@ -135,7 +135,7 @@

References

-[BLGN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., +[BLN+05] Beals, R., Leedham-Green, C. R., Niemeyer, A. C., Praeger, C. E. and Seress, Á., Constructive recognition of finite alternating and symmetric groups acting as matrix groups on their natural permutation modules, @@ -149,7 +149,7 @@

References

-[BLS97] Babai, L., Luks, E. M. and Seress, Á., +[BLS97] Babai, L., Luks, E. M. and Seress, Á., Fast management of permutation groups. I, SIAM J. Comput., 26 (5) @@ -161,7 +161,7 @@

References

-[BNS06] Brooksbank, P., Niemeyer, A. C. and Seress, Á., +[BNS06] Brooksbank, P., Niemeyer, A. C. and Seress, Á., A reduction algorithm for matrix groups with an extraspecial normal subgroup, in Finite geometries, groups, and computation, @@ -173,7 +173,7 @@

References

-[Bro01] Brooksbank, P. A., +[Bro01] Brooksbank, P. A., A constructive recognition algorithm for the matrix group \(\Omega(d,q)\), in Groups and computation, III (Columbus, OH, @@ -188,7 +188,7 @@

References

-[Bro03] Brooksbank, P. A., +[Bro03] Brooksbank, P. A., Fast constructive recognition of black-box unitary groups, LMS J. Comput. Math., 6 @@ -200,7 +200,7 @@

References

-[Bro08] Brooksbank, P. A., +[Bro08] Brooksbank, P. A., Fast constructive recognition of black box symplectic groups, J. Algebra, 320 (2) @@ -212,7 +212,7 @@

References

-[BS01] Babai, L. and Shalev, A., +[BS01] Babai, L. and Shalev, A., Recognizing simplicity of black-box groups and the frequency of \(p\)-singular elements in affine groups, in Groups and computation, III (Columbus, OH, @@ -227,7 +227,7 @@

References

-[CFL97] Cooperman, G., Finkelstein, L. and Linton, S., +[CFL97] Cooperman, G., Finkelstein, L. and Linton, S., Constructive recognition of a black box group isomorphic to \({\rm GL}(n,2)\), in Groups and computation, II (New Brunswick, @@ -242,7 +242,7 @@

References

-[CLG97a] Celler, F. and Leedham-Green, C. R., +[CL97a] Celler, F. and Leedham-Green, C. R., Calculating the order of an invertible matrix, in Groups and computation, II (New Brunswick, NJ, 1995), @@ -256,7 +256,7 @@

References

-[CLG97b] Celler, F. and Leedham-Green, C. R., +[CL97b] Celler, F. and Leedham-Green, C. R., A non-constructive recognition algorithm for the special linear and other classical groups, in Groups and computation, II (New Brunswick, @@ -271,7 +271,7 @@

References

-[CLG98] Celler, F. and Leedham-Green, C. R., +[CL98] Celler, F. and Leedham-Green, C. R., A constructive recognition algorithm for the special linear group, in The atlas of finite groups: ten years on (Birmingham, @@ -287,7 +287,7 @@

References

-[CLG01] Conder, M. and Leedham-Green, C. R., +[CL01] Conder, M. and Leedham-Green, C. R., Fast recognition of classical groups over large fields, in Groups and computation, III (Columbus, OH, 1999), @@ -301,7 +301,7 @@

References

-[CLGM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A., +[CLM+95] Celler, F., Leedham-Green, C. R., Murray, S. H., Niemeyer, A. C. and O'Brien, E. A., Generating random elements of a finite group, Comm. Algebra, 23 (13) @@ -313,7 +313,7 @@

References

-[CLGO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., +[CLO06] Conder, M. D. E., Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of \({\rm PSL}(2,q)\), Trans. Amer. Math. Soc., 358 (3) @@ -325,7 +325,7 @@

References

-[CNRD09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., +[CNR09] Carlson, J. F., Neunhöffer, M. and Roney-Dougal, C. M., A polynomial-time reduction algorithm for groups of semilinear or subfield class, J. Algebra, @@ -338,7 +338,7 @@

References

-[DLGLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., +[DLLO13] Dietrich, H., Leedham-Green, C. R., Lübeck, F. and O'Brien, E. A., Constructive recognition of classical groups in even characteristic, J. Algebra, @@ -351,7 +351,7 @@

References

-[DLGO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., +[DLO15] Dietrich, H., Leedham-Green, C. R. and O'Brien, E. A., Effective black-box constructive recognition of classical groups, J. Algebra, @@ -364,7 +364,7 @@

References

-[GH97] Glasby, S. P. and Howlett, R. B., +[GH97] Glasby, S. P. and Howlett, R. B., Writing representations over minimal fields, Comm. Algebra, 25 (6) @@ -376,7 +376,7 @@

References

-[GLGO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., +[GLO06] Glasby, S. P., Leedham-Green, C. R. and O'Brien, E. A., Writing projective representations over subfields, J. Algebra, 295 (1) @@ -386,9 +386,21 @@

References

+

+

+[HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A., + Constructive membership in black-box groups, + J. Group Theory, + 11 (6) + (2008), + 747–763
+(https://doi.org/10.1515/JGT.2008.047). +

+ +

-[HLGOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., +[HLOR96a] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Computing matrix group decompositions with respect to a normal subgroup, J. Algebra, @@ -401,7 +413,7 @@

References

-[HLGOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., +[HLOR96b] Holt, D. F., Leedham-Green, C. R., O'Brien, E. A. and Rees, S., Testing matrix groups for primitivity, J. Algebra, 184 (3) @@ -411,21 +423,9 @@

References

-

-

-[HLO+08] Holmes, P. E., Linton, S. A., O'Brien, E. A., Ryba, A. J. E. and Wilson, R. A., - Constructive membership in black-box groups, - J. Group Theory, - 11 (6) - (2008), - 747–763
-(https://doi.org/10.1515/JGT.2008.047). -

- -

-[HR94] Holt, D. F. and Rees, S., +[HR94] Holt, D. F. and Rees, S., Testing modules for irreducibility, J. Austral. Math. Soc. Ser. A, 57 (1) @@ -436,7 +436,7 @@

References

-[IL00] Ivanyos, G. and Lux, K., +[IL00] Ivanyos, G. and Lux, K., Treating the exceptional cases of the MeatAxe, Experiment. Math., 9 (3) @@ -448,7 +448,7 @@

References

-[JLNP13] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W., +[JLNP13] Jambor, S., Leuner, M., Niemeyer, A. C. and Plesken, W., Fast recognition of alternating groups of unknown degree, J. Algebra, 392 @@ -460,7 +460,7 @@

References

-[KK15] Kantor, W. M. and Kassabov, M., +[KK15] Kantor, W. M. and Kassabov, M., Black box groups isomorphic to \(\rm {PGL}(2,2^e)\), J. Algebra, 421 @@ -472,7 +472,7 @@

References

-[KM13] Kantor, W. M. and Magaard, K., +[KM13] Kantor, W. M. and Magaard, K., Black box exceptional groups of Lie type, Trans. Amer. Math. Soc., 365 (9) @@ -484,7 +484,7 @@

References

-[KM15] Kantor, W. M. and Magaard, K., +[KM15] Kantor, W. M. and Magaard, K., Black box exceptional groups of Lie type II, J. Algebra, 421 @@ -496,7 +496,7 @@

References

-[KS09] Kantor, W. M. and Seress, Á., +[KS09] Kantor, W. M. and Seress, Á., Large element orders and the characteristic of Lie-type simple groups, J. Algebra, @@ -509,7 +509,7 @@

References

-[LG01] Leedham-Green, C. R., +[Lee01] Leedham-Green, C. R., The computational matrix group project, in Groups and computation, III (Columbus, OH, 1999), @@ -521,9 +521,34 @@

References

+

+

+[LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A., + Constructive recognition of \({\rm SL}_3(q)\), + J. Algebra, + 316 (2) + (2007), + 619–633
+(https://doi.org/10.1016/j.jalgebra.2007.01.020). +

+ + +

+

+[LNPS06] Law, M., Niemeyer, A. C., Praeger, C. E. and Seress, Á., + A reduction algorithm for large-base primitive permutation + groups, + LMS J. Comput. Math., + 9 + (2006), + 159–173
+(https://doi.org/10.1112/S1461157000001236). +

+ +

-[LGO97a] Leedham-Green, C. R. and O'Brien, E. A., +[LO97a] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor products of matrix groups, Internat. J. Algebra Comput., 7 (5) @@ -535,7 +560,7 @@

References

-[LGO97b] Leedham-Green, C. R. and O'Brien, E. A., +[LO97b] Leedham-Green, C. R. and O'Brien, E. A., Tensor products are projective geometries, J. Algebra, 189 (2) @@ -547,7 +572,7 @@

References

-[LGO02] Leedham-Green, C. R. and O'Brien, E. A., +[LO02] Leedham-Green, C. R. and O'Brien, E. A., Recognising tensor-induced matrix groups, J. Algebra, 253 (1) @@ -557,9 +582,21 @@

References

+

+

+[LO07] Liebeck, M. W. and O'Brien, E. A., + Finding the characteristic of a group of Lie type, + J. Lond. Math. Soc. (2), + 75 (3) + (2007), + 741–754
+(https://doi.org/10.1112/jlms/jdm028). +

+ +

-[LGO09] Leedham-Green, C. R. and O'Brien, E. A., +[LO09] Leedham-Green, C. R. and O'Brien, E. A., Constructive recognition of classical groups in odd characteristic, J. Algebra, @@ -570,46 +607,9 @@

References

-

-

-[LMO07] Lübeck, F., Magaard, K. and O'Brien, E. A., - Constructive recognition of \({\rm SL}_3(q)\), - J. Algebra, - 316 (2) - (2007), - 619–633
-(https://doi.org/10.1016/j.jalgebra.2007.01.020). -

- - -

-

-[LNPS06] Law, M., Niemeyer, A. C., Praeger, C. E. and Seress, Á., - A reduction algorithm for large-base primitive permutation - groups, - LMS J. Comput. Math., - 9 - (2006), - 159–173
-(https://doi.org/10.1112/S1461157000001236). -

- - -

-

-[LO07] Liebeck, M. W. and O'Brien, E. A., - Finding the characteristic of a group of Lie type, - J. Lond. Math. Soc. (2), - 75 (3) - (2007), - 741–754
-(https://doi.org/10.1112/jlms/jdm028). -

- -

-[LO16] Liebeck, M. W. and O'Brien, E. A., +[LO16] Liebeck, M. W. and O'Brien, E. A., Recognition of finite exceptional groups of Lie type, Trans. Amer. Math. Soc., 368 (9) @@ -632,7 +632,7 @@

References

-[Nie05] Niemeyer, A. C., +[Nie05] Niemeyer, A. C., Constructive recognition of normalizers of small extra-special matrix groups, Internat. J. Algebra Comput., @@ -645,7 +645,7 @@

References

-[NP92] Neumann, P. M. and Praeger, C. E., +[NP92] Neumann, P. M. and Praeger, C. E., A recognition algorithm for special linear groups, Proc. London Math. Soc. (3), 65 (3) @@ -657,7 +657,7 @@

References

-[NP97] Niemeyer, A. C. and Praeger, C. E., +[NP97] Niemeyer, A. C. and Praeger, C. E., Implementing a recognition algorithm for classical groups, in Groups and computation, II (New Brunswick, NJ, 1995), @@ -671,7 +671,7 @@

References

-[NP98] Niemeyer, A. C. and Praeger, C. E., +[NP98] Niemeyer, A. C. and Praeger, C. E., A recognition algorithm for classical groups over finite fields, Proc. London Math. Soc. (3), @@ -684,7 +684,7 @@

References

-[NP99] Niemeyer, A. C. and Praeger, C. E., +[NP99] Niemeyer, A. C. and Praeger, C. E., A recognition algorithm for non-generic classical groups over finite fields, J. Austral. Math. Soc. Ser. A, @@ -696,7 +696,7 @@

References

-[NS06] Neunhöffer, M. and Seress, Á., +[NS06] Neunhöffer, M. and Seress, Á., A data structure for a uniform approach to computations with finite groups, in ISSAC 2006, @@ -710,7 +710,7 @@

References

-[O'B06] O'Brien, E. A., +[O'B06] O'Brien, E. A., Towards effective algorithms for linear groups, in Finite geometries, groups, and computation, Walter de Gruyter, Berlin @@ -721,7 +721,7 @@

References

-[O'B11] O'Brien, E. A., +[O'B11] O'Brien, E. A., Algorithms for matrix groups, in Groups St Andrews 2009 in Bath. Volume 2, @@ -735,7 +735,7 @@

References

-[Pak00] Pak, I., +[Pak00] Pak, I., The product replacement algorithm is polynomial, in 41st Annual Symposium on Foundations of Computer @@ -749,7 +749,7 @@

References

-[Par84] Parker, R. A., +[Par84] Parker, R. A., The computer calculation of modular characters (the meat-axe), in Computational group theory (Durham, 1982), Academic Press, London @@ -760,7 +760,7 @@

References

-[Pra99] Praeger, C. E., +[Pra99] Praeger, C. E., Primitive prime divisor elements in finite classical groups, in Groups St. Andrews 1997 in Bath, II, @@ -775,7 +775,7 @@

References

-[Ser03] Seress, Á., +[Ser03] Seress, Á., Permutation group algorithms, Cambridge University Press, Cambridge, Cambridge Tracts in Mathematics, @@ -794,6 +794,6 @@

References

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diff --git a/doc/chapInd.txt b/doc/chapInd.txt index 0bd29f56..3ec0fcb0 100644 --- a/doc/chapInd.txt +++ b/doc/chapInd.txt @@ -26,8 +26,8 @@ FindKernelDoNothing 3.2-28 FindKernelFastNormalClosure 3.2-29 FindKernelRandom 3.2-27 - forfactor 8. - forkernel 8. + forfactor 8.0 + forkernel 8.0 gensN 3.2-25 gensNslp 3.2-30 Grp 3.2-6 @@ -41,10 +41,10 @@ isone 3.2-34 IsReady 3.2-5 IsRecogMethod 4.1-1 - IsRecognitionInfo 8. + IsRecognitionInfo 8.0 IsRecogNode 3.2-2 KernelRecogNode 3.2-11 - methodsforfactor 8. + methodsforfactor 8.0 methodsforimage 3.2-17 NiceGens 3.2-8 OrderFunc 3.2-36 @@ -56,7 +56,7 @@ RecogniseMatrixGroup 3.1-3 RecognisePermGroup 3.1-2 RecogniseProjectiveGroup 3.1-4 - RecognitionInfoFamily 8. + RecognitionInfoFamily 8.0 RecognizeGeneric 3.1-1 RecognizeGroup 3.1-5 RecognizeMatrixGroup 3.1-3 @@ -64,9 +64,9 @@ RecognizeProjectiveGroup 3.1-4 RecogNode 3.2-3 3.2-3 RecogNodeFamily 3.2-1 - RIFac 8. - RIKer 8. - RIParent 8. + RIFac 8.0 + RIKer 8.0 + RIParent 8.0 Size 5.1-3 slpforelement 3.2-14 SLPforElement 3.2-15 diff --git a/doc/chapInd_mj.html b/doc/chapInd_mj.html index 685afce1..5da2edf3 100644 --- a/doc/chapInd_mj.html +++ b/doc/chapInd_mj.html @@ -6,7 +6,7 @@ GAP (recog) - Index @@ -117,6 +117,6 @@

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