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

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.