Arithmetic trialitarian hyperbolic lattices are not LERF
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914731355275264 |
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| author | Bogachev, Nikolay Slavich, Leone Sun, Hongbin |
| author_facet | Bogachev, Nikolay Slavich, Leone Sun, Hongbin |
| contents | A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that all arithmetic lattices in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, are not LERF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20611 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arithmetic trialitarian hyperbolic lattices are not LERF Bogachev, Nikolay Slavich, Leone Sun, Hongbin Group Theory Geometric Topology Number Theory A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that all arithmetic lattices in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, are not LERF. |
| title | Arithmetic trialitarian hyperbolic lattices are not LERF |
| topic | Group Theory Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2310.20611 |