Expansion in perfect groups

Details Expansion in perfect groups Expansion in perfect groups

2011-08-24

arxiv.org/abs/1108.4900v2

Mathematics

Group Theory

61 pages, no figures, revised introduction, new references added, results unchanged

Scientific paper

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.

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