منابع مشابه
Relatively hyperbolic Groups
In this paper we develop some of the foundations of the theory of relatively hyperbolic groups as originally formulated by Gromov. We prove the equivalence of two definitions of this notion. One is essentially that of a group admitting a properly discontinuous geometrically finite action on a proper hyperbolic space, that is, such that every limit point is either a conical limit point or a boun...
متن کاملGrowth of relatively hyperbolic groups
We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth. Mathematics Subject Classification(2000). 20F65.
متن کاملEndomorphisms of Relatively Hyperbolic Groups
We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. • If H is a non-parabolic subgroup of a relatively hyperb...
متن کاملLimit Groups for Relatively Hyperbolic
We begin the investigation of Γ-limit groups, where Γ is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of [16], we adapt the results from [21] and [22] to this context. Specifically, given a finitely generated group G, and a sequence of pairwise non-conjugate homomorphisms {hn : G → Γ}, we extract anR-tree with a nontrivial isomet...
متن کاملOn definitions of relatively hyperbolic groups
The purpose of this note is to provide a short alternate proof of the fact that [9, Question 1] has an affirmative answer. Our proof combined with the result of Szczepanski [9] shows that a group which is relatively hyperbolic in the sense of the definition of Gromov is relatively hyperbolic in the sense of the definition of Farb.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2018
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089518000423