ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 05 Sep 2013 14:17:55 -0500Elementary abelian p-subgroups of a finite grouphttp://ask.sagemath.org/question/10515/elementary-abelian-p-subgroups-of-a-finite-group/Let G be a finite group. An elementary abelian p-subgroup of G is an abelian subgroup E whose exponent is p. The order of such a group is p^r from some r, called the rank of E. The lattice of all elementary abelian p-subgroups in G is called the Quillen Complex of the group G. I'm interested in using Sage to obtain some information about the Quillen Complex such as:
1. For a fixed r, how many conjugacy classes of elementary abelian p-subgroups of rank r are in G?
2. How many such subgroups are in each conjugacy class?
3. What is a set of minimal generators of a subgroup representing each conjugacy class?
In short, Magma has a command called ElementaryAbelianSubgroups which does exactly what I want, but I'd like to figure out how to do this with Sage. I'm very new to Sage, so I would appreciate as much detail in your answer as possible.
Perhaps someone has already dealt with this question, and I can benefit from their work, or perhaps there are similar commands that I can combine to answer my question.Thu, 05 Sep 2013 14:17:55 -0500http://ask.sagemath.org/question/10515/elementary-abelian-p-subgroups-of-a-finite-group/