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Abstract: Babai and S\-os have asked whether there exists a constant c>0 such thatevery 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 thispaper we show that the answer is no. Moreover, we give a simple sufficientcondition for a group not to have any large product-free subset.

Author: W. T. Gowers

Source: https://arxiv.org/

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