Quasirandom groups
Combinatorics
2007-10-23 v1 Group Theory
Abstract
Babai and S\'os have asked whether there exists a constant c>0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy=z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.
Cite
@article{arxiv.0710.3877,
title = {Quasirandom groups},
author = {W. T. Gowers},
journal= {arXiv preprint arXiv:0710.3877},
year = {2007}
}
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31 pages