2007/08/16 by Kiran S. Kedlaya, Kedlaya, Kiran S. · 1 citation
Computer Science · Mathematics · #20D60 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.CO #math.GR #msc:20D60
paper · pdf · doi:10.48550/arxiv.0708.2295
9 pages; from conference "Communicating Mathematics" in honor of Joe Gallian (Duluth, 2007); v2: refereed version, very minor revisions
openalex publication_date 2007/08/16 · arxiv created 2007/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.