JournalsggdVol. 5, No. 2pp. 509–527

Words and mixing times in finite simple groups

  • Gili Schul

    The Hebrew University of Jerusalem, Israel
  • Aner Shalev

    The Hebrew University of Jerusalem, Israel
Words and mixing times in finite simple groups cover
Download PDF

Abstract

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

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

Cite this article

Gili Schul, Aner Shalev, Words and mixing times in finite simple groups. Groups Geom. Dyn. 5 (2011), no. 2, pp. 509–527

DOI 10.4171/GGD/137