Product-free subsets of groups, then and now
| dc.creator | Kedlaya, Kiran S. | |
| dc.date | 2007-08-16 | |
| dc.date | 2007-11-07 | |
| dc.date.accessioned | 2026-07-07T08:40:54Z | |
| dc.date.available | 2026-07-07T08:40:54Z | |
| dc.description | 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. | |
| dc.description | 9 pages; from conference "Communicating Mathematics" in honor of Joe Gallian (Duluth, 2007); v2: refereed version, very minor revisions | |
| dc.identifier | https://arxiv.org/abs/0708.2295 | |
| dc.identifier | http://arxiv.org/abs/0708.2295 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141513 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20D60 | |
| dc.title | Product-free subsets of groups, then and now | |
| dc.type | text |