Article ID Journal Published Year Pages File Type
4587764 Journal of Algebra 2008 12 Pages PDF
Abstract

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 2(xG) 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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory