Uniform expansion in finite groups of Lie type

2026/08/01 by Oren Becker, Emmanuel Breuillard
Mathematics · #math.GR #msc:20D06 #msc:05C48 #msc:14G15

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arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

We prove that finite simple groups G(p) of bounded rank and with p prime have uniform expansion, that is, the family of all the Cayley graphs forms a family of (two-sided) expanders, except perhaps when p belongs to a small family of exceptional primes. Furthermore, for all prime powers q, the set of possible exceptions to uniform expansion of G(q) is shown to have ``dimension zero''. We also extend these results to semisimple and perfect algebraic groups.

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