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

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.

12 pages, to appear in J. Pure Appl. Algebra

References in corpus (5)

• Non-positively curved aspects of Artin groups of finite type
• Garside groups are strongly translation discrete
• Some power of an element in a Garside group is conjugate to a periodically geodesic element
• Abelian subgroups of Garside groups
• Stable super summit sets in Garside groups

Cited by in corpus (10)

• A Garside-theoretic approach to the reducibility problem in braid groups
• Braid groups of imprimitive complex reflection groups
• Braid groups and Artin groups
• Some power of an element in a Garside group is conjugate to a periodically geodesic element
• Abelian subgroups of Garside groups
• Periodic elements in Garside groups
• Conjugacy classes of periodic braids
• Locally elliptic actions, torsion groups, and nonpositively curved spaces
• Notes on periodic elements of Garside groups
• Acylindricity of the action of right-angled Artin groups on extension graphs