Abelian subgroups of Garside groups

Details Abelian subgroups of Garside groups Abelian subgroups of Garside groups

2006-09-25

arxiv.org/abs/math/0609683v3

Communications in Algebra, vol. 36, no. 3, pp. 1121-1139, 2008

Mathematics

Geometric Topology

This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/0602582

Scientific paper

10.1080/00927870701715605

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. 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.

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