[GAP Forum] extensions of subgroups of a finite 2-group
Petr Savicky
savicky at cs.cas.cz
Wed Jul 16 15:39:06 BST 2014
Dear GAP Forum:
Assume, G is a finite 2-group and A is its subgroup.
The groups may be permutation groups or pc groups.
I would like to construct all extensions B of A, such
that [B:A] = 2.
One way is to perform
N := Normalizer(G, A);
R := RightTransversal(N, A);
L := [];
for elm in R do
if elm in A then
continue;
fi;
if elm^2 in A then
Add(L, ClosureGroup(A, elm));
fi;
od;
Is there a better way?
Another question is as follows. Let G be a 2-group
and H and A its subgroups, such that the intersection
of H and A is trivial. Is it possible to determine
in GAP, whether there is a subgroup B of G, such
that B contains A and is a complement of H in G?
I appreciate any help concerning these questions.
Best regards,
Petr Savicky.
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