On the product decomposition conjecture for finite simple groups

Gill, Nick; Pyber, László; Short, Ian and Szabó, Endre (2013). On the product decomposition conjecture for finite simple groups. Groups, Geometry, and Dynamics, 7(4) pp. 867–882.

DOI: https://doi.org/10.4171/GGD/208

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|/|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 bounded rank. We also obtain various related results about products of conjugates of a set within a group.

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