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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.07757 |
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| _version_ | 1866909629910351872 |
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| author | Bridson, Martin R. |
| author_facet | Bridson, Martin R. |
| contents | For every natural number $n$, there exist finitely presented groups with residual finiteness depths $ω\cdot n$ and $ω\cdot n + 1$. The ordinals that arise as the residual finiteness depth of a finitely generated group (equivalently, a countable group) are $0,\, 1$, the countable limit ordinals, and the successors of these limit ordinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ordinals arising as residual finiteness depths Bridson, Martin R. Group Theory 20E26, 20E06, 20E08 For every natural number $n$, there exist finitely presented groups with residual finiteness depths $ω\cdot n$ and $ω\cdot n + 1$. The ordinals that arise as the residual finiteness depth of a finitely generated group (equivalently, a countable group) are $0,\, 1$, the countable limit ordinals, and the successors of these limit ordinals. |
| title | Ordinals arising as residual finiteness depths |
| topic | Group Theory 20E26, 20E06, 20E08 |
| url | https://arxiv.org/abs/2411.07757 |