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27 changes: 14 additions & 13 deletions lib/grppcext.gi
Original file line number Diff line number Diff line change
Expand Up @@ -370,12 +370,12 @@ local ag, p1iso, agp, p2iso, DP, p1, p2, gens, genimgs, triso,s,i,u,opt,

# are both groups solvable?
p2iso:=IsomorphismPermGroup(DirectProductInfo(D).groups[2]);
gp2:=ImagesSource(p2iso);
gp2:=Image(p2iso,DirectProductInfo(D).groups[2]);
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fingolfin marked this conversation as resolved.
if IsSolvableGroup(gp2) and IsSolvableGroup(agp) then
# both groups are solvable -- go solvable
pc1:=IsomorphismPcGroup(agp);
pc2:=IsomorphismPcGroup(gp2);
DP:=DirectProduct(ImagesSource(pc1),ImagesSource(pc2));
DP:=DirectProduct(Image(pc1,agp),Image(pc2,gp2));
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fingolfin marked this conversation as resolved.
p1:=Projection(DP,1);
p2:=Projection(DP,2);
gens:=Pcgs(DP);
Expand Down Expand Up @@ -528,7 +528,6 @@ local G, M, Mgrp, oper, A, B, D, translate, gens, genimgs, triso, K, K1,
if A=fail and Length(arg)=2 then
# search through automorphism group for projection image and reps,
# then add module automorphisms
gens:=GeneratorsOfGroup(G);
if A=fail then
Info( InfoCompPairs, 1, " CompP: compute aut group");
A:=AutomorphismGroup(G);
Expand All @@ -538,22 +537,22 @@ local G, M, Mgrp, oper, A, B, D, translate, gens, genimgs, triso, K, K1,
direct:=true;
fi;

elif A=fail and Length(arg)=3 and HasDirectProductInfo(arg[3])
and IsGroupOfAutomorphismsFiniteGroup(Image(Projection(arg[3],1))) then
elif A=fail and Length(arg)=3 and HasDirectProductInfo(arg[3]) then

A:=Image(Projection(arg[3],1));
B:=Image(Projection(arg[3],2));
u:=B;
gens:=GeneratorsOfGroup(G);
if Size(A)>1 and Size(B)>1 and Size(A)*Size(B)>1000 then
A:=DirectProductInfo(arg[3]).groups[1];
B:=DirectProductInfo(arg[3]).groups[2];

if IsGroupOfAutomorphismsFiniteGroup(A) and Size(A)>1 and Size(B)>1 and Size(A)*Size(B)>1000 then
direct:=true;
u:=B;
else
A:=fail;
fi;

elif IsPcgs(Ggens) and Length(Ggens)=Length(M.generators) then
oper := GroupHomomorphismByImagesNC( G, Mgrp, Ggens, M.generators );
fi;

if direct then
gens:=GeneratorsOfGroup(G);
triso:=NiceMonomorphism(A:autactbase:=fail);
if not IsPermGroup(Image(triso)) then
triso:=IsomorphismPermGroup(A:autactbase:=fail);
Expand Down Expand Up @@ -586,7 +585,7 @@ local G, M, Mgrp, oper, A, B, D, translate, gens, genimgs, triso, K, K1,
B:=Difference(B,[i]);
fi;
od;
K:=Group(GeneratorsOfGroup(K){B});
K:=Group(GeneratorsOfGroup(K){B}, One(K));
pool:=pool{B};

B:=MTX.ModuleAutomorphisms(M);
Expand Down Expand Up @@ -616,6 +615,8 @@ local G, M, Mgrp, oper, A, B, D, translate, gens, genimgs, triso, K, K1,
return A;
fi;

elif IsPcgs(Ggens) and Length(Ggens)=Length(M.generators) then
oper := GroupHomomorphismByImagesNC( G, Mgrp, Ggens, M.generators );
fi;

if oper=fail then
Expand Down
23 changes: 23 additions & 0 deletions tst/testbugfix/2026-08-14-AutomorphismGroupSolvableGroup.tst
Original file line number Diff line number Diff line change
@@ -0,0 +1,23 @@
# Several errors or wrong results were briefly produced by
# AutomorphismGroup respectively AutomorphismGroupSolvableGroup.
# See https://github.com/gap-system/gap/pull/6510
gap> START_TEST("2026-08-14-AutomorphismGroupSolvableGroup.tst");

#
gap> Size(AutomorphismGroup(SmallGroup(24,3)));
24
gap> Size(AutomorphismGroup(SmallGroup(147, 4)));
98784
gap> Size(AutomorphismGroup(SmallGroup(864,4675)));
10368

#
gap> Size(AutomorphismGroupSolvableGroup(SmallGroup(24,3)));
24
gap> Size(AutomorphismGroupSolvableGroup(SmallGroup(147, 4)));
98784
gap> Size(AutomorphismGroupSolvableGroup(SmallGroup(864,4675)));
10368

#
gap> STOP_TEST("2026-08-14-AutomorphismGroupSolvableGroup.tst");
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