Translation numbers in a Garside group are rational with uniformly bounded denominators
arXiv:math/0604061 · doi:10.1016/j.jpaa.2007.04.003
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