Back to Search
Start Over
Conjugacy geodesics and growth in dihedral Artin groups
- Publication Year :
- 2024
-
Abstract
- In this paper we describe conjugacy geodesic representatives in any dihedral Artin group $G(m)$, $m\geq 3$, which we then use to calculate asymptotics for the conjugacy growth of $G(m)$, and show that the conjugacy growth series of $G(m)$ with respect to the `free product' generating set $\{x, y\}$ is transcendental. This, together with recent results on Artin groups and contracting elements, implies that all Artin groups of XXL-type have transcendental conjugacy growth series for some generating set. We prove two additional properties of $G(m)$ that connect to conjugacy, namely that the permutation conjugator length function is constant, and that the falsification by fellow traveler property (FFTP) holds with respect to $\{x, y\}$. These imply that the language of all conjugacy geodesics in $G(m)$ with respect to $\{x, y\}$ is regular.
- Subjects :
- Mathematics - Group Theory
20E45, 20F36, 05E16
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.17312
- Document Type :
- Working Paper