Separability properties of higher-rank GBS groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913670213140480 |
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| author | Zearra, Jone Lopez de Gamiz Shepherd, Sam |
| author_facet | Zearra, Jone Lopez de Gamiz Shepherd, Sam |
| contents | A rank $n$ generalized Baumslag-Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. In this paper we classify these groups in terms of their separability properties. Specifically, we determine when they are residually finite, subgroup separable and cyclic subgroup separable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14527 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separability properties of higher-rank GBS groups Zearra, Jone Lopez de Gamiz Shepherd, Sam Group Theory 20F65 (Primary) 20E26, 20E08 (Secondary) A rank $n$ generalized Baumslag-Solitar group is a group that splits as a finite graph of groups such that all vertex and edge groups are isomorphic to $\mathbb{Z}^n$. In this paper we classify these groups in terms of their separability properties. Specifically, we determine when they are residually finite, subgroup separable and cyclic subgroup separable. |
| title | Separability properties of higher-rank GBS groups |
| topic | Group Theory 20F65 (Primary) 20E26, 20E08 (Secondary) |
| url | https://arxiv.org/abs/2309.14527 |