Maróti Attila: A generalization of the diameter bound of Liebeck and Shalev for finite simple groups

Abstract. Let G be a non-abelian finite simple group and S a subset of G of size at least 2 which is a union of conjugacy classes in G. A famous theorem of Liebeck and Shalev, from 2001, states that there is a universal constant c such that whenever k is an integer at least c*(log|G|/log|S|) then S^k is equal to G. We will talk about a generalization of this result. It is joint work with László Pyber. We will also talk about a continuation of this paper concerning alternating groups. This is joint work with Martino Garonzi.

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