Groups with a complemented presentation
type: Item
instance of: scholarly article
title: Groups with a complemented presentation
zbMATH Open document ID: 0870.20023
DOI: 10.1016/S0022-4049(96)00074-6
author: Patrick Dehornoy
published in: Journal of Pure and Applied Algebra
publication date: 1997-09-08T00:00:00Z
review text: A presentation of a group is said to be right complemented if for any two generators \(x\) and \(y\), there exists one relation of the form \(xu=yv\), where \(u\) and \(v\) are finite products of generators, and furthermore any relation in the presentation is such a relation. Artin's braid groups are an important example. The author investigates such groups and presents a simple quadratic algorithm for solving their word problem.
reviewed by: Steven C. Althoen
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F36
zbMATH DE Number: 1004394
zbMATH Keywords: right complemented presentations
zbMATH Keywords: generators
zbMATH Keywords: relations
zbMATH Keywords: Artin's braid groups
zbMATH Keywords: quadratic algorithms
zbMATH Keywords: word problems
MaRDI profile type: Publication
cites work: Braids, Links, and Mapping Class Groups. (AM-82)
cites work: Q3848243
cites work: Q4015542
cites work: Braid Groups and Left Distributive Operations
cites work: The structure group for the associativity identity
cites work: Q4385532
cites work: ALGORITHMS FOR POSITIVE BRAIDS
cites work: Q4003861
cites work: Q5580926
cites work: THE BRAID GROUP AND OTHER GROUPS
cites work: Braid group actions on left distributive structures, and well orderings in the braid groups
cites work: An Isoperimetric Inequality for Artin Groups of Finite Type
description: scientific article; zbMATH DE number 1004394