Product-free subsets of groups, then and now

Details Product-free subsets of groups, then and now Product-free subsets of groups, then and now

2007-08-16

arxiv.org/abs/0708.2295v2

Mathematics

Group Theory

9 pages; from conference "Communicating Mathematics" in honor of Joe Gallian (Duluth, 2007); v2: refereed version, very minor

Scientific paper

A subset of a group is product-free if it does not contain elements a, b, c such that ab = c. We review progress on the problem of determining the size of the largest product-free subset of an arbitrary finite group, including a lower bound due to the author, and a recent upper bound due to Gowers. The bound of Gowers is more general; it allows three different sets A, B, C such that one cannot solve ab = c with a in A, b in B, c in C. We exhibit a refinement of the lower bound construction which shows that for this broader question, the bound of Gowers is essentially optimal.

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