Parabolic subgroups of Artin groups

DOI10.1006/jabr.1997.7098zbMath0926.20022OpenAlexW2043357595MaRDI QIDQ1372632

Luis Paris

Publication date: 1 December 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7098

zbMATH Keywords

parabolic subgroupsArtin groupscommensuratorsquasi-centralizersArtin systems

Mathematics Subject Classification ID

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

Related Items (30)

Commensurability in Artin groups of spherical type ⋮ Artin groups of spherical type up to isomorphism. ⋮ Rewriting systems in sufficiently large Artin-Tits groups. ⋮ Conjugacy in relatively extra-large Artin groups ⋮ Artin-Tits groups with CAT(0) Deligne complex. ⋮ Centralizers of parabolic subgroups of Artin groups of type \(A_l\), \(B_l\), and \(D_l\) ⋮ Conjugacy stability of parabolic subgroups of Artin-Tits groups of spherical type ⋮ On the growth of Artin-Tits monoids and the partial theta function ⋮ Birth of Garside groups in memory of Patrick Dehornoy ⋮ Extra-large type Artin groups are hierarchically hyperbolic ⋮ Parabolic subgroups in FC-type Artin groups ⋮ Normalizer and Artin group of spherical type. ⋮ Parabolic Deligne-Lusztig varieties ⋮ Surface subgroups of Coxeter and Artin groups. ⋮ Parabolic subgroups acting on the additional length graph ⋮ Parabolic subgroups of Garside groups. ⋮ Second mod 2 homology of Artin groups ⋮ Presentations for the punctured mapping class groups in terms of Artin groups ⋮ Abstract commensurators of braid groups. ⋮ Braids, their Properties and Generalizations ⋮ Relative hyperbolicity and Artin groups. ⋮ Conjugacy in singular Artin monoids ⋮ Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity. ⋮ On the minimal positive standardizer of a parabolic subgroup of an Artin-Tits group ⋮ Artin groups of infinite type: Trivial centers and acylindrical hyperbolicity ⋮ Hyperbolic structures for Artin-Tits groups of spherical type ⋮ The conjugacy stability problem for parabolic subgroups in Artin groups ⋮ On parabolic submonoids of a class of singular Artin monoids ⋮ Parabolic subgroups of large-type Artin groups ⋮ Parabolic subgroups inside parabolic subgroups of Artin groups

Cites Work

• Artin groups and infinite Coxeter groups
• The conjugacy problem for Coxeter groups.
• Braid subgroup normalisers, commensurators and induced representations
• The homotopy type of Artin groups
• Centralisers in the braid group and singular braid monoid
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• Conjugacy classes of involutions in Coxeter groups
• Normalizers of Parabolic Subgroups of Reflection Groups
• On the root system of a coxeter group
• Commensurators of parabolic subgroups of Coxeter groups
• The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1
• The K(π, 1)-Problem for Hyperplane Complements Associated to Infinite Reflection Groups
• THE BRAID GROUP AND OTHER GROUPS
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