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Fix an error in MinimalFaithfulPermutationDegree, for the case of abelian direct factors #5730

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May 28, 2024
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Fix an error in MinimalFaithfulPermutationDegree, for the case of abelian direct factors #5730

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17 changes: 10 additions & 7 deletions lib/grplatt.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -3467,13 +3467,13 @@ end);
BindGlobal("DoMinimalFaithfulPermutationDegree",
function(G,dorep)
local c,n,deg,ind,core,i,j,sum,ma,h,ig,bm,m,sel,ds,ise,cnt,
start,cind,nind,sl,idfun,spos,select,bla;
start,cind,nind,sl,idfun,spos,select,bla,iswith;

if Size(G)=1 then
# option allows to calculate actual representation -- maybe access under
# different name
if dorep=false then
return 1;
return 0;
else
return GroupHomomorphismByImages(G,Group(()),[One(G)],[()]);
fi;
Expand Down Expand Up @@ -3555,10 +3555,7 @@ local c,n,deg,ind,core,i,j,sum,ma,h,ig,bm,m,sel,ds,ise,cnt,
ind:=IndexNC(G,c[i]);
spos:=PositionSorted(sl,Size(c[i]))-1;


if i in sel then
# do nothing --already processed
elif IsNormal(G,c[i]) then # subgroup normal, must be in other case
if IsNormal(G,c[i]) then # subgroup normal, must be in other case
#core:=Position(n,c[i]);
core:=nind[i];

Expand All @@ -3569,7 +3566,13 @@ local c,n,deg,ind,core,i,j,sum,ma,h,ig,bm,m,sel,ds,ise,cnt,
#Print("|select|=",Length(select),"\n");
fi;

for j in [2..core-1] do # Intersect with all prior normals
iswith:=[2..core-1]; # what to intersect with
# avoid intersecting abelians -- there might be many
if i in sel then
iswith:=Difference(iswith,nind{sel});
fi;

for j in iswith do # Intersect with all prior normals
sum:=deg[core][1]+deg[j][1];
if sum<deg[Length(n)][1] then # otherwise too big for new optimal
if select=fail then
Expand Down
3 changes: 3 additions & 0 deletions tst/testbugfix/2024-05-28-Mindeg.tst
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Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
# Fix #5729
gap> MinimalFaithfulPermutationDegree(SmallGroup(42,3));
10
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