2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140459Babai 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.31 pagesCombinatoricsGroup Theory05D05;20C15text