Generalizations of product-free subsets
| dc.creator | Kedlaya, Kiran S. | |
| dc.creator | Shao, Xuancheng | |
| dc.date | 2008-04-04 | |
| dc.date.accessioned | 2026-07-07T09:30:26Z | |
| dc.date.available | 2026-07-07T09:30:26Z | |
| dc.description | For any group G of order n, a subset A of G is said to be product-free if there is no solution of the equation ab=c with a,b,c in A. Previous results of Gowers showed that the size of any product-free subset of G is at most n/d^(1/3), where d is the smallest dimension of a nontrivial representation of G. However, this upper bound does not match the best lower bound. We will generalize the upper bound to the case of product-poor subsets A, in which the equation ab=c is allowed to have a few solutions with a,b,c in A. We prove that the upper bound for the size of product-poor subsets matches the best lower bound in many families of groups. We will also generalize the concept of product-free to the case in which we have many subsets of a group, and different constraints about products of the elements in the subsets. | |
| dc.description | 8 pages; from conference "Communicating Mathematics" in honor of Joe Gallian (Duluth, 2007); related to 0708.2295 | |
| dc.identifier | https://arxiv.org/abs/0804.0687 | |
| dc.identifier | http://arxiv.org/abs/0804.0687 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158125 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20D60 | |
| dc.title | Generalizations of product-free subsets | |
| dc.type | text |