A finitely presented torsion-free simple group
| dc.creator | Rattaggi, Diego | |
| dc.date | 2004-11-24 | |
| dc.date.accessioned | 2026-07-07T05:14:39Z | |
| dc.date.available | 2026-07-07T05:14:39Z | |
| dc.description | We construct a finitely presented torsion-free simple group $Σ_0$, acting cocompactly on a product of two regular trees. An infinite family of such groups has been introduced by Burger-Mozes ([2,4]). We refine their methods and get $Σ_0$ as an index 4 subgroup of a group $Σ< \mathrm{Aut}(\mathcal{T}_{12}) \times \mathrm{Aut}(\mathcal{T}_{8})$ presented by 10 generators and 24 short relations. For comparison, the smallest virtually simple group of [4, Theorem 6.4] needs more than 18000 relations, and the smallest simple group constructed in [4, Section 6.5] needs even more than 360000 relations in any finite presentation. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0411546 | |
| dc.identifier | http://arxiv.org/abs/math/0411546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73359 | |
| dc.subject | Group Theory | |
| dc.title | A finitely presented torsion-free simple group | |
| dc.type | text |