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 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
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