Normalizer and Artin group of spherical type.

DOI10.1016/S0021-8693(03)00529-5zbMath1060.20032OpenAlexW2081716155MaRDI QIDQ1414041

Eddy Godelle

Publication date: 19 November 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-8693(03)00529-5

zbMATH Keywords

parabolic subgroupsCoxeter groupsArtin groupsnormalizerscommensuratorsquasi-centralizersassociated monoids

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Free semigroups, generators and relations, word problems (20M05) Braid groups; Artin groups (20F36) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (19)

On centralizers of parabolic subgroups in Coxeter groups ⋮ Centralisers in Surface Braid Groups ⋮ Artin-Tits groups with CAT(0) Deligne complex. ⋮ Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type ⋮ Parabolic subgroups in FC-type Artin groups ⋮ The center of pure complex braid groups. ⋮ Parabolic Deligne-Lusztig varieties ⋮ Parabolic subgroups acting on the additional length graph ⋮ Parabolic subgroups of Garside groups. ⋮ Parabolic subgroups of Garside groups. II: Ribbons. ⋮ Abstract commensurators of braid groups. ⋮ Conjugacy in singular Artin monoids ⋮ On parabolic subgroups of Artin-Tits groups of spherical type ⋮ On the minimal positive standardizer of a parabolic subgroup of an Artin-Tits group ⋮ Quasicentralizer of LCM-Homomorphisms ⋮ Tits alternative for Artin groups of type FC ⋮ The conjugacy stability problem for parabolic subgroups in Artin groups ⋮ Parabolic subgroups of large-type Artin groups ⋮ Parabolic subgroups inside parabolic subgroups of Artin groups

Cites Work

• The conjugacy problem for Coxeter groups.
• Fragments of the word \(\Delta\) in a braid group
• A note on words in braid monoids
• Geodesic automation and growth functions for Artin groups of finite type
• Parabolic subgroups of Artin groups
• Artin monoids inject in their groups
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• Normalizers of Parabolic Subgroups of Reflection Groups
• On the root system of a coxeter group
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
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