# Garside group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

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## Contents

## History

### Origin

The notion of Garside group was inspired by Garside's work on the solvable word problem and the solvable conjugacy problem for braind groups and Artin groups, and was an attempt ata lattice-theoretic generalization of these. The notion was first introduced in *Gaussian groups and Garside groups, two generalisations of Artin groups* by Dehernoy and Paris, in 1999.

### Further work

Sang Jin Lee has recently proved that Garside groups are strongly translation-discrete.

## Definition

A **Garside group** is a group that occurs as the group of fractions of a Garside monoid (note that the group of fractions is guaranteed to exist because any Garside monoid satisfies Ore's conditions).

## Relation with other properties

### Stronger properties

- Braid group
- Artin group of finite type