Growth of products of subsets in finite simple groups

Dona, Daniele and Maróti, Attila and Pyber, László (2024) Growth of products of subsets in finite simple groups. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. Early View. ISSN 0024-6093

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Abstract

We prove that the product of a subset and a normal subset inside any finite simple non-abelian group G grows rapidly. More precisely, if A and B are two subsets with B normal and neither of them is too large inside G, then |AB| ≥ |A||B|1-ϵ where ϵ > 0 can be taken arbitrarily small. This is a somewhat surprising strengthening of a theorem of Liebeck, Schul, and Shalev.

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