All hyperbolic cyclically presented groups with positive length three relators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911256401674240 |
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| author | Chinyere, Ihechukwu Edjvet, Martin Williams, Gerald |
| author_facet | Chinyere, Ihechukwu Edjvet, Martin Williams, Gerald |
| contents | We consider the cyclically presented groups defined by cyclic presentations with $2m$ generators $x_i$ whose relators are the $2m$ positive length three relators $x_ix_{i+1}x_{i+m-1}$. We show that they are hyperbolic if and only if $m\in \{1,2,3,6,9\}$. This completes the classification of the hyperbolic cyclically presented groups with positive length three relators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All hyperbolic cyclically presented groups with positive length three relators Chinyere, Ihechukwu Edjvet, Martin Williams, Gerald Group Theory 20F05, 20F06, 20F67 We consider the cyclically presented groups defined by cyclic presentations with $2m$ generators $x_i$ whose relators are the $2m$ positive length three relators $x_ix_{i+1}x_{i+m-1}$. We show that they are hyperbolic if and only if $m\in \{1,2,3,6,9\}$. This completes the classification of the hyperbolic cyclically presented groups with positive length three relators. |
| title | All hyperbolic cyclically presented groups with positive length three relators |
| topic | Group Theory 20F05, 20F06, 20F67 |
| url | https://arxiv.org/abs/2408.09903 |