Dear Petr,
I don't see how your first question is related to the group G. If you
want ALL extensions of A with a group of order 2, you could use
CyclicExtensions(A,2) from the GrpConst package. However, if A is small,
it is much faster to run through the groups of order 2|A| in the small
groups library and check which groups have maximal subgroups isomorphic
to A (i.e. the same GroupID).
I don't have any good advice concerning your second question.
Best,
Benjamin
Am 16.07.2014 16:39, schrieb Petr Savicky:
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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