Products and commutators of classes in algebraic groups
Group Theory
2013-03-22 v2
Abstract
We classify pairs of conjugacy classes in almost simple algebraic groups whose product consists of finitely many classes. This leads to several interesting families of examples which are related to a generalization of the Baer--Suzuki theorem for finite groups. We also answer a question of Pavel Shumyatsky on commutators of pairs of conjugacy classes in simple algebraic groups. It turns out that the resulting examples are exactly those for which the product also consists of only finitely many classes.
Cite
@article{arxiv.1302.0182,
title = {Products and commutators of classes in algebraic groups},
author = {Robert Guralnick and Gunter Malle},
journal= {arXiv preprint arXiv:1302.0182},
year = {2013}
}