Gaussian groups are torsion free

DOI10.1006/jabr.1998.7540zbMath0959.20035OpenAlexW1994300421MaRDI QIDQ1276989

Patrick Dehornoy

Publication date: 2 May 2001

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

Full work available at URL: https://semanticscholar.org/paper/c23b6b070218ed09dbc052ebf380b5693d04fb75

zbMATH Keywords

cancellative monoidsgroups of fractionstorsion free groupsfinite Coxeter type Artin groups

Mathematics Subject Classification ID

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

Related Items (21)

Decomposition of Garside groups and self-similar \(L\)-algebras ⋮ Artin groups of spherical type up to isomorphism. ⋮ Birth of Garside groups in memory of Patrick Dehornoy ⋮ Homology of Gaussian groups. ⋮ The geometry of discrete \(L\)-algebras ⋮ Abelian Subgroups of Garside Groups ⋮ The Yang–Baxter equation and Thompson’s group F ⋮ Complete positive group presentations. ⋮ Periodic elements in Garside groups. ⋮ A Garside-theoretic approach to the reducibility problem in braid groups. ⋮ The structure group of an \(L\)-algebra is torsion-free ⋮ THE CONJUGACY PROBLEM IN SMALL GAUSSIAN GROUPS ⋮ Injectivity on the set of conjugacy classes of some monomorphisms between Artin groups. ⋮ The group of fractions of a torsion free lcm monoid is torsion free. ⋮ The language of geodesics for Garside groups ⋮ The center of thin Gaussian groups ⋮ Translation numbers in a Garside group are rational with uniformly bounded denominators. ⋮ Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation ⋮ Garside Groups and Yang–Baxter Equation ⋮ PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY ⋮ Groupes de Garside

Cites Work

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• Groups with a complemented presentation
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• An Isoperimetric Inequality for Artin Groups of Finite Type
• BRAIDS, ORDERINGS AND ZERO DIVISORS
• Braid Groups and Left Distributive Operations
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
• THE BRAID GROUP AND OTHER GROUPS

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