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Preprint Number 1470

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1470. Daniel Palacín
On compactifications and product-free sets
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Submission date: 26 July 2018

Abstract:

A subset of a group is said to be product-free if it does not contain three elements satisfying the equation xy=z. We give a negative answer to a question of Babai and Sós on the existence of large product-free sets by model theoretic means. This question was originally answered by Gowers. Furthermore, we give a natural and sufficient model theoretic condition for a group to have a large product-free subset, as well as a model theoretic account of a result of Nikolov and Pyber on triple products.

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Full text arXiv 1807.10113: pdf, ps.


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