We prove that if is a finite simple group of Lie type and is a subset of of size at least two, then is a product of at most conjugates of , where depends only on the Lie rank of . 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.
Cite this article
Nick Gill, László Pyber, Ian Short, Endre Szabó, On the product decomposition conjecture for finite simple groups. Groups Geom. Dyn. 7 (2013), no. 4, pp. 867–882DOI 10.4171/GGD/208