Higman-Thompson groups and profinite properties of right-angled Coxeter groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866908697850019840 |
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| author | Corson, Samuel M. Hughes, Sam Möller, Philip Varghese, Olga |
| author_facet | Corson, Samuel M. Hughes, Sam Möller, Philip Varghese, Olga |
| contents | We prove that every right-angled Coxeter group (RACG) is profinitely rigid amongst all Coxeter groups. On the other hand we exhibit RACGs which have infinite profinite genus amongst all finitely generated residually finite groups. We also establish profinite rigidity results for graph products of finite groups. Along the way we prove that the Higman-Thompson groups $V_{n}$ are generated by $4$ involutions, generalising a classical result of Higman for Thompson's group $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06213 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higman-Thompson groups and profinite properties of right-angled Coxeter groups Corson, Samuel M. Hughes, Sam Möller, Philip Varghese, Olga Group Theory Primary: 20F55, 20E18, Secondary: 20E36, 20F65, 20E45 We prove that every right-angled Coxeter group (RACG) is profinitely rigid amongst all Coxeter groups. On the other hand we exhibit RACGs which have infinite profinite genus amongst all finitely generated residually finite groups. We also establish profinite rigidity results for graph products of finite groups. Along the way we prove that the Higman-Thompson groups $V_{n}$ are generated by $4$ involutions, generalising a classical result of Higman for Thompson's group $V$. |
| title | Higman-Thompson groups and profinite properties of right-angled Coxeter groups |
| topic | Group Theory Primary: 20F55, 20E18, Secondary: 20E36, 20F65, 20E45 |
| url | https://arxiv.org/abs/2309.06213 |