Elementary subgroups of relatively hyperbolic groups and bounded generation
| dc.creator | Osin, D. V. | |
| dc.date | 2004-04-06 | |
| dc.date.accessioned | 2026-07-07T05:07:12Z | |
| dc.date.available | 2026-07-07T05:07:12Z | |
| dc.description | Let $G$ be a group hyperbolic relative to a collection of subgroups $\{H_λ,λ\in Λ\} $. We say that a subgroup $Q\le G$ is hyperbolically embedded into $G$, if $G$ is hyperbolic relative to $\{H_λ,λ\in Λ\} \cup \{Q\} $. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an element $g\in G$ has infinite order and is not conjugate to an element of $H_λ$, $λ\in Λ$, then the (unique) maximal elementary subgroup contained $g$ is hyperbolically embedded into $G$. This allows to prove that if $G$ is boundedly generated, then $G$ is elementary or $H_λ=G$ for some $λ\in Λ$. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404118 | |
| dc.identifier | http://arxiv.org/abs/math/0404118 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70763 | |
| dc.subject | Group Theory | |
| dc.subject | 20F65; 20F67; 20F69 | |
| dc.title | Elementary subgroups of relatively hyperbolic groups and bounded generation | |
| dc.type | text |