Groups, Geometry, and Dynamics


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Volume 5, Issue 2, 2011, pp. 509–527
DOI: 10.4171/GGD/137

Published online: 2011-03-06

Words and mixing times in finite simple groups

Gili Schul[1] and Aner Shalev[2]

(1) The Hebrew University of Jerusalem, Israel
(2) The Hebrew University of Jerusalem, Israel

Let $w \neq$ 1 be a non-trivial group word, let $G$ be a finite simple group, and let $w(G)$ be the set of values of $w$ in $G$. We show that if $G$ is large, then the random walk on $G$ with respect to $w(G)$ as a generating set has mixing time 2.

This strengthens various known results, for example the fact that $w(G)^2$ covers almost all of $G$.

Keywords: Words, random walks, finite simple groups, mixing time

Schul Gili, Shalev Aner: Words and mixing times in finite simple groups. Groups Geom. Dyn. 5 (2011), 509-527. doi: 10.4171/GGD/137