# Quasirandom Groups

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

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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