On compactifications and product-free sets
Group Theory
2019-07-31 v2 Combinatorics
Logic
Abstract
A subset of a group is said to be product-free if it does not contain three elements satisfying the equation . We give a negative answer to a question of Babai and S\'os 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.
Keywords
Cite
@article{arxiv.1807.10113,
title = {On compactifications and product-free sets},
author = {Daniel Palacín},
journal= {arXiv preprint arXiv:1807.10113},
year = {2019}
}