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On compactifications and product‐free sets
Journal of the London Mathematical Society ( IF 1.121 ) Pub Date : 2019-07-24 , DOI: 10.1112/jlms.12263
Daniel Palacín

A subset of a group is said to be product free if it does not contain three elements satisfying the equation x y = z . We give a negative answer to a question of Babai and Sós on the existence of large product‐free sets in finite groups 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.
更新日期:2020-04-23

 

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