Groups with a complemented presentation. (English) Zbl 0870.20023

Dehornoy, Patrick

J. Pure Appl. Algebra 116, No. 1-3, 115-137 (1997).

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.

Reviewer: S.C.Althoen (Flint)

MSC:

20F05	Generators, relations, and presentations of groups
20F10	Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F36	Braid groups; Artin groups

Keywords:

right complemented presentations; generators; relations; Artin’s braid groups; quadratic algorithms; word problems

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