Mixing and generation in simple groups

Let G be a finite simple group. We show that a random walk on G with respect to the conjugacy class x G of a random element x ∈ G has mixing time 2. In particular it follows that ( x G ) 2 covers almost all of G, which could be regarded as a probabilistic version of a longstanding conjecture of Thom...

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Bibliographic Details
Published inJournal of algebra Vol. 319; no. 7; pp. 3075 - 3086
Main Author Shalev, Aner
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2008
Subjects
Characters
Finite simple groups
Probabilistic methods
Random walks
Word maps
Word maps
Probabilistic methods
Finite simple groups
Random walks
Characters
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Summary:Let G be a finite simple group. We show that a random walk on G with respect to the conjugacy class x G of a random element x ∈ G has mixing time 2. In particular it follows that ( x G ) 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2007.07.031