A Strong Tits Alternative
| dc.creator | Breuillard, Emmanuel | |
| dc.date | 2008-04-09 | |
| dc.date.accessioned | 2026-07-07T09:31:16Z | |
| dc.date.available | 2026-07-07T09:31:16Z | |
| dc.description | We show that for every integer $d$, there is a constant $N(d)$ such that if $K$ is any field and $F$ is a finite subset of $GL_d(K)$, which generates a non amenable subgroup, then $F^{N(d)}$ contains two elements, which freely generate a non abelian free subgroup. This improves the original statement of the Tits alternative. It also implies a growth gap and a co-growth gap for non-amenable linear groups, and has consequences about the girth and uniform expansion of small sets in finite subgroups of $GL_d(\Bbb{F}_q)$ as well as other diophantine properties of non-discrete subgroups of Lie groups. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/0804.1395 | |
| dc.identifier | http://arxiv.org/abs/0804.1395 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158401 | |
| dc.subject | Group Theory | |
| dc.subject | 20G25 ; 22E40 | |
| dc.title | A Strong Tits Alternative | |
| dc.type | text |