All hyperbolic cyclically presented groups with positive length three relators
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.09903
- arXiv:
- arXiv:2408.09903
- Bibcode:
- 2024arXiv240809903C
- Keywords:
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- Mathematics - Group Theory;
- 20F05;
- 20F06;
- 20F67
- E-Print:
- 45 pages including 11 figures