English

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.

Keywords

Cite

@article{arxiv.0710.3877,
  title  = {Quasirandom groups},
  author = {W. T. Gowers},
  journal= {arXiv preprint arXiv:0710.3877},
  year   = {2007}
}

Comments

31 pages

R2 v1 2026-06-21T09:34:20.299Z