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arXiv · 2504.15636

Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups

Laura Ciobanu·Anthony Genevois
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Abstract

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.

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Laura Ciobanu, Anthony Genevois. 2025-04-22. Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups. https://arxiv.org/abs/2504.15636

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