Abelian subgroups of Garside groups
Geometric Topology
2008-07-23 v3 Group Theory
Abstract
In this paper, we show that for every abelian subgroup of a Garside group, some conjugate consists of ultra summit elements and the centralizer of is a finite index subgroup of the normalizer of . Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.
Cite
@article{arxiv.math/0609683,
title = {Abelian subgroups of Garside groups},
author = {Eon-Kyung Lee and Sang Jin Lee},
journal= {arXiv preprint arXiv:math/0609683},
year = {2008}
}
Comments
This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/0602582