Bounded subgroups of relatively finitely presented groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914862841462784 |
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| author | Schesler, Eduard |
| author_facet | Schesler, Eduard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12638 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounded subgroups of relatively finitely presented groups Schesler, Eduard Group Theory Metric Geometry 20F67, 20F65 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. |
| title | Bounded subgroups of relatively finitely presented groups |
| topic | Group Theory Metric Geometry 20F67, 20F65 |
| url | https://arxiv.org/abs/2203.12638 |