On the product decomposition conjecture for finite simple groups

Abstract

We prove that if $G$ is a finite simple group of Lie type and $S$ a subset of $G$ of size at least two then $G$ is a product of at most $c\log |G|/\log |S|$ conjugates of $S$, where $c$ depends only on the Lie rank of $G$. This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of Lie type of bounded rank.

13 pages. In this version a number of new results are added which generalize some classical results of additive combinatorics to the non-abelian setting

References in corpus (1)

• Finite Simple Groups as Expanders

Cited by in corpus (1)

• Growth in linear groups