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On a question of Babai and Sós, a model theoretic approach

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In 1985, Babai and Sós asked whether there exists a constant c>0 such that every finite group of order n has a product-free set of size at least cn, where a product-free set of a group is a subset that does not contain three elements x, y and z satisfying xy=z. Gowers showed that the answer is no in the early 2000s, by linking the existence of product-free sets of large density to the existence of low dimensional unitary representations.

In this talk, I will explain how one can answer the aforementioned question using model theoretic ideas, and relate the existence of product-free sets of large density to the existence of certain non-trivial group compactifications

This talk is part of the Discrete Analysis Seminar series.

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