Abelian subgroups of Garside groups

Eon-Kyung Lee; Sang Jin Lee

doi:10.1080/00927870701715605

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arXiv · math/0609683

Abelian subgroups of Garside groups

Eon-Kyung Lee·Sang Jin Lee

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Abstract

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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BibTeX RIS

Eon-Kyung Lee, Sang Jin Lee. 2008-07-23. Abelian subgroups of Garside groups. https://doi.org/10.1080/00927870701715605

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