Geometric and Functional Analysis

, Volume 20, Issue 5, pp 1201-1209

First online:

Strong Uniform Expansion in SL(2, p)

  • Emmanuel BreuillardAffiliated withLaboratoire de Mathématiques, Université Paris-Sud 11 Email author 
  • , Alex GamburdAffiliated withDepartment of Mathematics, University of California at Santa Cruz

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We show that there is an infinite set of primes \({\mathcal P}\) of density one, such that the family of all Cayley graphs of SL(2, p), \({p \in \mathcal P,}\) is a family of expanders.

Keywords and phrases

Expander graphs Tits alternative random walks finite groups

2010 Mathematics Subject Classification

20G40 20N99 60B99