Quasirandom Groups

@article{Gowers2008QuasirandomG,
  title={Quasirandom Groups},
  author={W. T. Gowers},
  journal={Combinatorics, Probability and Computing},
  year={2008},
  volume={17},
  pages={363 - 387}
}
  • W. T. Gowers
  • Published 2008
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
Babai and Sós 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. 
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