Large Product-Free Subsets of Finite Groups

A subset of a group is said to beproduct-freeif the product of two of its elements is never itself an element of the subset. Using the classification of finite simple groups, we prove that every finite group of ordernhas a product-free subset of more thancn11/14elements, for some fixedc>0. This improves on a lower bound of Babai and Sَs.