I believe that
ConjugacyClassesSubgroups(LatticeByCyclicExtension(g, IsElementaryAbelian,
true));
Does what you want.
Steve
On 6 Sep 2013, at 10:24, "Ellis, Grahamj" <graham.el...@nuigalway.ie> wrote:
> Dear GAP forum,
>
> I too would like to know how best to access the elementary abelian
> p-subgroups of a finite group G. Attached is an implementation of the Quillen
> Complex which uses ConjugacyClassesSubgroups. As Jared mentions, this is a
> very inefficient approach.
>
> ------------------------------------------------------------------------
> gap> G:=SmallGroup(64,134);;
> gap> Q:=QuillenComplex(G,2);
> Simplicial complex of dimension 2.
>
> gap> Homology(Q,0);
> [ 0 ]
> gap> Homology(Q,1);
> [ ]
> gap> Homology(Q,2);
> [ ]
> gap> Q!.nrSimplices(2); #The number of 2-simplices
> 168
> gap> Q!.simplices(2,168); #The last 2-simplex
> [ Group([ f6, f2, f3*f4*f5 ]), Group([ f2, f3*f4*f5*f6 ]),
> Group([ f2*f3*f4*f5*f6 ]) ]
> ------------------------------------------------------------------------
>
>
> Graham
>
> School of Mathematics, Statistics & Applied Mathematics
> National University of Ireland, Galway
> University Road,
> Galway
> Ireland
>
> http://hamilton.nuigalway.ie
> tel: 091 493011
> ________________________________________
> From: forum-boun...@gap-system.org [forum-boun...@gap-system.org] on behalf
> of Jared Warner [jaredwarn...@gmail.com]
> Sent: Friday, September 06, 2013 1:32 AM
> To: fo...@gap-system.org
> Subject: [GAP Forum] Elementary abelian p-subgroups
>
> Dear GAP forum,
>
> I'm interested in studying the Quillen Complex of a finite group G, which
> is the lattice of elementary abelian p-subgroups of G. Magma has a command
> ElementaryAbelianSubgroups which does exactly what I want, but I'd like to
> do this with GAP (to avoid paying for Magma).
>
> Specifically, given a finite group G I'd like to know:
>
> 1. The number of conjugacy classes of elementary abelian p-subgroups of a
> certain rank
>
> 2. The number of subgroups in each such conjugacy class
>
> 3. A set of generators of a representative from each such conjugacy class
>
> I'm aware of ConjugacyClassesSubgroups, but I'd like to my command return a
> list of representatives of elementary abelian p-subgroups, not all
> subgroups.
>
> Also, I'd like to avoid working with ConjugacyClassesSubgroups if possible,
> because it seems like a lot of wasted time and memory to compute the whole
> subgroup lattice when I'm only interested in a small portion of it.
>
> Thanks for any help!
>
> Jared
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