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Speed up AutomorphismGroup for solvable Frattini-free groups #6500

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Merged
fingolfin merged 1 commit into from
Aug 14, 2026
+17 −1
Merged

Speed up AutomorphismGroup for solvable Frattini-free groups #6500

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4 changes: 3 additions & 1 deletion lib/morpheus.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -2491,7 +2491,9 @@ local A;
#LoadPackage("autpgrp"); # try to load the package if it exists
A:=AutomorphismGroupNilpotentGroup(G);
elif IsSolvableGroup(G) then
if HasIsFrattiniFree(G) and IsFrattiniFree(G) then
# AutomorphismGroupFrattFreeGroup needs a pcgs for subgroups of G, which
# is not available for example for finitely presented groups
if CanEasilyComputePcgs(G) and IsFrattiniFree(G) then
A:=AutomorphismGroupFrattFreeGroup(G);
else
# currently autactbase does not work well, as the representation might
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14 changes: 14 additions & 0 deletions tst/testinstall/opers/AutomorphismGroup.tst
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Expand Up @@ -24,8 +24,22 @@ true
# solvable group
gap> G:=DihedralGroup(100);
<pc group of size 100 with 4 generators>
gap> IsFrattiniFree(G);
false
gap> AutomorphismGroup(G);
<group of size 1000 with 4 generators>

# solvable Frattini-free groups, handled by AutomorphismGroupFrattFreeGroup
gap> G:=SymmetricGroup(4);;
gap> IsFrattiniFree(G);
true
gap> Size(AutomorphismGroup(G));
24
gap> Size(AutomorphismGroup(SymmetricGroup(IsPcGroup,4)));
24
gap> G:=Group((1,2,3,4,5),(2,3,5,4));; # Frobenius group of order 20
gap> Size(AutomorphismGroup(G));
20

#
gap> STOP_TEST("AutomorphismGroup.tst");
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