Translation numbers in a Garside group are rational with uniformly bounded denominators

2006/04/30 by Eon-Kyung Lee, Eon Kyung Lee, Sangjin Lee +1 · 1 citation
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F10 #msc:20F36

paper · pdf · doi:10.1016/j.jpaa.2007.04.003

published as Journal of Pure and Applied Algebra, vol. 211, no. 3, pp. 732-743, 2007 · 12 pages, to appear in J. Pure Appl. Algebra

arxiv created 2007/03/22 · openalex publication_date 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an application, we give solutions to some group-theoretic problems.

Citations

• Stable super summit sets in Garside groups
• Artin-Gruppen und Coxeter-Gruppen
• Gaussian Groups are Torsion Free
• ALGORITHMS FOR POSITIVE BRAIDS
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups

Cited by

• Abelian Subgroups of Garside Groups
• A Garside-theoretic approach to the reducibility problem in braid groups