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- Title
ELEMENTARY SUBGROUPS OF RELATIVELY HYPERBOLIC GROUPS AND BOUNDED GENERATION.
- Authors
Osin, Denis V.
- Abstract
Let G be a group hyperbolic relative to a collection of subgroups {Hλ, λ ∈ Λ}. We say that a subgroup Q ≤ G is hyperbolically embedded into G, if G is hyperbolic relative to {Hλ, λ ∈ Λ} ∪ {Q}. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an element g ∈ G has infinite order and is not conjugate to an element of some Hλ, λ ∈ Λ, then the (unique) maximal elementary subgroup containing g is hyperbolically embedded into G. This allows us to prove that if G is boundedly generated, then G is elementary or Hλ = G for some λ ∈ Λ.
- Subjects
HYPERBOLIC groups; GROUP theory; HYPERBOLIC spaces; NON-Euclidean geometry; PRODUCTS of subgroups; MATHEMATICAL analysis; ALGEBRA
- Publication
International Journal of Algebra & Computation, 2006, Vol 16, Issue 1, p99
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196706002901