Finite quotients of groups of I-type

Abstract

To every group of $I$-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the particular case of groups of I-type. Groups of $I$-type are related to finite set theoretical solutions of the Yang-Baxter equation.

References in corpus (6)

• Set-theoretical solutions to the quantum Yang-Baxter equation
• On set-theoretical solutions of the quantum Yang-Baxter equation
• Semigroups of I-type
• Garside groups and Yang-Baxter equation
• Braces and the Yang-Baxter equation
• Coxeter-like groups for groups of set-theoretic solutions of the Yang--Baxter equation

Cited by in corpus (9)

• On structure groups of set-theoretic solutions to the Yang-Baxter equation
• Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova
• About left orders in Garside groups
• Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces
• Involutive latin solutions of the Yang-Baxter equation
• Retractability of solutions to the Yang-Baxter equation and $p$-nilpotency of skew braces
• The Yang-Baxter equation and Thompson's group $F$
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• A note on Garside monoids and Braces