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Bounded subgroups of relatively finitely presented groups

Eduard Schesler

Algebraic & Geometric Topology 24 (2024) 1551–1567
Abstract

Let G be a finitely generated group that is relatively finitely presented with respect to a collection HΛ of peripheral subgroups such that the corresponding relative Dehn function is well defined. We prove that every infinite subgroup H of G that is bounded in the relative Cayley graph of G with respect to HΛ is conjugate into a peripheral subgroup. As an application, we obtain a trichotomy for subgroups of relatively hyperbolic groups. Moreover we prove the existence of the relative exponential growth rate for all subgroups of limit groups.

Keywords
relatively finitely presented groups, relatively hyperbolic groups, growth of groups, coarse geometry
Mathematical Subject Classification
Primary: 20F67
References
Publication
Received: 18 March 2022
Revised: 1 February 2023
Accepted: 1 March 2023
Published: 28 June 2024
Authors
Eduard Schesler
Fakultät für Mathematik und Informatik
FernUniversität in Hagen
Hagen
Germany

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