Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910022394445824 |
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| author | Genevois, Anthony |
| author_facet | Genevois, Anthony |
| contents | In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we propose a combinatorial geometry (mediangle graphs) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06421 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups Genevois, Anthony Group Theory Combinatorics Metric Geometry 20F65, 20F67, 05C25 In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we propose a combinatorial geometry (mediangle graphs) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups. |
| title | Rotation groups, mediangle graphs, and periagroups: a unified point of view on Coxeter groups and graph products of groups |
| topic | Group Theory Combinatorics Metric Geometry 20F65, 20F67, 05C25 |
| url | https://arxiv.org/abs/2212.06421 |