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arXiv · 2203.12638

Bounded subgroups of relatively finitely presented groups

Eduard Schesler
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Abstract

Given a finitely generated group $G$ that is relatively finitely presented with respect to a collection of peripheral subgroups, we prove that every infinite subgroup $H$ of $G$ that is bounded in the relative Cayley graph of $G$ 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.

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Eduard Schesler. 2022-03-23. Bounded subgroups of relatively finitely presented groups. https://doi.org/10.2140/agt.2024.24.1551

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