[GAP Forum] extensions of subgroups of a finite 2-group

[Benjamin Sambale]

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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