Mixing and generation in simple groups

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Let G be a finite simple group. We show that a random walk on G with respect to the conjugacy class xG of a random element x ∈ G has mixing time 2. In particular it follows that (xG)2 covers almost all of G, which could be regarded as a probabilistic version of a longstanding conjecture of Thompson. We also show that if w is a non-trivial word, then almost every pair of values of w in G generates G.

Original languageAmerican English
Pages (from-to)3075-3086
Number of pages12
JournalJournal of Algebra
Issue number7
StatePublished - 1 Apr 2008

Bibliographical note

Funding Information:
✩ Supported by the Israel Science Foundation and by the Bi-National Science Foundation United States–Israel Grant 2004-052. E-mail address: shalev@math.huji.ac.il.


  • Characters
  • Finite simple groups
  • Probabilistic methods
  • Random walks
  • Word maps


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