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Quasirandom Groups

Published online by Cambridge University Press:  01 May 2008

W. T. GOWERS
W. T. GOWERS*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: [email protected])
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Abstract

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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 363 - 387
Copyright
Copyright © Cambridge University Press 2008

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