When Do Random Subsets Decompose a Finite Group?
| dc.creator | Yadin, Ariel | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T08:50:07Z | |
| dc.date.available | 2026-07-07T08:50:07Z | |
| dc.description | Let A,B be two random subsets of a finite group G. We consider the event that the products of elements from A and B span the whole group; i.e. (AB union BA) = G. The study of this event gives rise to a group invariant we call Θ(G). Θ(G) is between 1/2 and 1, and is 1 if and only if the group is abelian. We show that a phase transition occurs as the size of A and B passes \sqrt{Θ(G)|G|\log|G|}; i.e. for any c>0, if the size of A and B is less than (1-c)\sqrt{Θ(G)|G|\log|G|}, then with high probability (AB union BA) does not equal G. If A and B are larger than (1+c)\sqrt{Θ(G)|G|\log|G|} then (AB union BA) equals G with high probability. | |
| dc.identifier | https://arxiv.org/abs/0712.3019 | |
| dc.identifier | http://arxiv.org/abs/0712.3019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144502 | |
| dc.subject | Probability | |
| dc.subject | Group Theory | |
| dc.subject | 60C05; 20P05 | |
| dc.title | When Do Random Subsets Decompose a Finite Group? | |
| dc.type | text |