Abelian Subgroups of Garside Groups

摘要

In this article, 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.View full textDownload full textKey WordsAbelian subgroup, Algebraic flat torus theorem, Conjugacy class, Garside group, Translation number2000 Mathematics Subject ClassificationPrimary 20F36, Secondary 20F10Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870701715605