Profinite rigidity of affine Coxeter groups
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917709831208960 |
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| author | Paolini, Gianluca Sklinos, Rizos |
| author_facet | Paolini, Gianluca Sklinos, Rizos |
| contents | We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-order theory of any irreducible affine Coxeter group does not have a prime model. Finally, we prove that universal Coxeter groups of finite rank are homogeneous, and that the same applies to every hyperbolic (in the sense of Gromov) one-ended right-angled Coxeter group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Profinite rigidity of affine Coxeter groups Paolini, Gianluca Sklinos, Rizos Group Theory Logic 03C60, 20F55 We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-order theory of any irreducible affine Coxeter group does not have a prime model. Finally, we prove that universal Coxeter groups of finite rank are homogeneous, and that the same applies to every hyperbolic (in the sense of Gromov) one-ended right-angled Coxeter group. |
| title | Profinite rigidity of affine Coxeter groups |
| topic | Group Theory Logic 03C60, 20F55 |
| url | https://arxiv.org/abs/2407.01141 |