Abelian subgroups of Garside groups

Eon-Kyung Lee; Sang Jin Lee

doi:10.1080/00927870701715605

Abelian subgroups of Garside groups

几何拓扑 2008-07-23 v3 群论

作者: Eon-Kyung Lee , Sang Jin Lee

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摘要

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.

关键词

finite group theory abelian groups additive combinatorics

引用

@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}
}

备注

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

Abelian subgroups of Garside groups

摘要

关键词

引用

备注

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