TY - UNPB
T1 - Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups
AU - Ciobanu, Laura
AU - Genevois, Anthony
N1 - 45 pages, 12 figures. Comments are welcome!
PY - 2025/4/22
Y1 - 2025/4/22
N2 - 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.
AB - 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.
KW - math.GR
KW - math.CO
KW - math.MG
KW - 20F65, 20F67, 20F55, 05C25
U2 - 10.48550/arXiv.2504.15636
DO - 10.48550/arXiv.2504.15636
M3 - Preprint
BT - Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups
PB - arXiv
ER -