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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.08353 |
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| _version_ | 1866913915632353280 |
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| author | Patil, Harsh |
| author_facet | Patil, Harsh |
| contents | We show that properties $F_n$ and $FP_n$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended groups that are type $F_n$ but not $F_{n+1}$ and similarly of type $FP_n$ and not $FP_{n+1}$ for all positive integers $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finiteness properties and Relatively Hyperbolic Groups Patil, Harsh Group Theory We show that properties $F_n$ and $FP_n$ hold for a relatively hyperbolic group if and only if they hold for all the peripheral subgroups. As an application we show that there are at least countably many distinct quasi-isometry classes of one-ended groups that are type $F_n$ but not $F_{n+1}$ and similarly of type $FP_n$ and not $FP_{n+1}$ for all positive integers $n$. |
| title | Finiteness properties and Relatively Hyperbolic Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2308.08353 |