Geometric and Functional Analysis

, Volume 20, Issue 5, pp 1201–1209

Strong Uniform Expansion in SL(2, p)


DOI: 10.1007/s00039-010-0094-3

Cite this article as:
Breuillard, E. & Gamburd, A. Geom. Funct. Anal. (2010) 20: 1201. doi:10.1007/s00039-010-0094-3


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 

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité Paris-Sud 11Orsay cedexFrance
  2. 2.Department of MathematicsUniversity of California at Santa CruzSanta CruzUSA

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