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Avoid IdGroup in IsSymmetricGroup #6383

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Merged
ThomasBreuer merged 2 commits into from
May 9, 2026
Merged

Avoid IdGroup in IsSymmetricGroup #6383

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Avoid IdGroup in IsSymmetricGroup
fingolfin May 3, 2026
ea50863
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fingolfin May 9, 2026
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19 changes: 14 additions & 5 deletions lib/grpnames.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1278,12 +1278,21 @@ InstallMethod( IsSymmetricGroup,
return true;
fi;

# the derived subgroup must be alternating and have index 2
G1 := DerivedSubgroup(G);
if not (IsAlternatingGroup(G1) and Index(G,G1) = 2)
# this requires deg>=4
or not IsTrivial(Centralizer(G,G1))
or Size(G) = 720 and IdGroup(G) <> [ 720, 763 ]
then return false; fi;
if not (IsAlternatingGroup(G1) and Index(G,G1) = 2) then
return false;
fi;
# the derived subgroup must have trivial centralizer (since degree >= 4)
if not IsTrivial(Centralizer(G,G1)) then
return false;
fi;
# one more special case: there are three groups of order 720 which satisfy
# the above, so here we need extra work to pick the correct one: it is
# only one in which all elements have order <= 6
if Size(G) = 720 and not ForAll(G,x->Order(x)<=6) then
return false;
fi;
SetSymmetricDegree(G,AlternatingDegree(G1));
return true;
end );
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