Right-angled Artin subgroups of right-angled Coxeter and Artin groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929324493373440 |
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| author | Dani, Pallavi Levcovitz, Ivan |
| author_facet | Dani, Pallavi Levcovitz, Ivan |
| contents | We determine when certain natural classes of subgroups of right-angled Coxeter groups (RACGs) and right-angled Artin groups (RAAGs) are themselves RAAGs. We characterize finite-index visual RAAG subgroups of 2-dimensional RACGs. As an application, we show that any 2-dimensional, one-ended RACG with planar defining graph is quasi-isometric to a RAAG if and only if it is commensurable to a RAAG. Additionally, we give new examples of RACGs with non-planar defining graphs which are commensurable to RAAGs.
Finally, we give a new proof of a result of Dyer: every subgroup generated by conjugates of RAAG generators is itself a RAAG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_05531 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Right-angled Artin subgroups of right-angled Coxeter and Artin groups Dani, Pallavi Levcovitz, Ivan Group Theory Geometric Topology 20F65, 20F55 We determine when certain natural classes of subgroups of right-angled Coxeter groups (RACGs) and right-angled Artin groups (RAAGs) are themselves RAAGs. We characterize finite-index visual RAAG subgroups of 2-dimensional RACGs. As an application, we show that any 2-dimensional, one-ended RACG with planar defining graph is quasi-isometric to a RAAG if and only if it is commensurable to a RAAG. Additionally, we give new examples of RACGs with non-planar defining graphs which are commensurable to RAAGs. Finally, we give a new proof of a result of Dyer: every subgroup generated by conjugates of RAAG generators is itself a RAAG. |
| title | Right-angled Artin subgroups of right-angled Coxeter and Artin groups |
| topic | Group Theory Geometric Topology 20F65, 20F55 |
| url | https://arxiv.org/abs/2003.05531 |