Submission date: 2 January 2020

Abstract:

We give a model-theoretic proof of a result of Shalev on probabilistically finite nilpotent groups. More generally, we prove that a group where the equation [x_1,...,x_k]=1 holds on a wide set, in a model theoretic sense, is an extension of a nilpotent group of class k by a uniformly locally finite group. In particular, this result applies to (definably) amenable groups, as well as to suitable model-theoretic families of definable groups such as groups in simple theories and groups with finitely satisfiable generics.

Mathematics Subject Classification:

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Full text arXiv 2001.00544: pdf, ps.