Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908331736563712 |
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| author | Ciobanu, Laura Genevois, Anthony |
| author_facet | Ciobanu, Laura Genevois, Anthony |
| contents | In this article we construct contracting elements in the standard Cayley graphs of the so-called periagroups, a family of groups introduced by the second-named author which include Coxeter groups, graph products, and Dyer groups. As a consequence, we deduce that, unless they virtually split as direct products, periagroups are acylindrically hyperbolic and their conjugacy growth series, with respect to standard generating sets, are transcendental. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups Ciobanu, Laura Genevois, Anthony Group Theory Combinatorics Metric Geometry 20F65, 20F67, 20F55, 05C25 In this article we construct contracting elements in the standard Cayley graphs of the so-called periagroups, a family of groups introduced by the second-named author which include Coxeter groups, graph products, and Dyer groups. As a consequence, we deduce that, unless they virtually split as direct products, periagroups are acylindrically hyperbolic and their conjugacy growth series, with respect to standard generating sets, are transcendental. |
| title | Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups |
| topic | Group Theory Combinatorics Metric Geometry 20F65, 20F67, 20F55, 05C25 |
| url | https://arxiv.org/abs/2504.15636 |