Abelian subgroups of Garside groups
| dc.creator | Lee, Eon-Kyung | |
| dc.creator | Lee, Sang Jin | |
| dc.date | 2006-09-25 | |
| dc.date | 2008-07-23 | |
| dc.date.accessioned | 2026-07-07T09:52:10Z | |
| dc.date.available | 2026-07-07T09:52:10Z | |
| dc.description | 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. | |
| dc.description | This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/0602582 | |
| dc.identifier | https://arxiv.org/abs/math/0609683 | |
| dc.identifier | http://arxiv.org/abs/math/0609683 | |
| dc.identifier | Communications in Algebra, vol. 36, no. 3, pp. 1121-1139, 2008 | |
| dc.identifier | doi:10.1080/00927870701715605 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165498 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F36; 20F10 | |
| dc.title | Abelian subgroups of Garside groups | |
| dc.type | text |