Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587764 | Journal of Algebra | 2008 | 12 Pages |
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