an:01004394
Zbl 0870.20023
Dehornoy, Patrick
Groups with a complemented presentation
EN
J. Pure Appl. Algebra 116, No. 1-3, 115-137 (1997).
00039604
1997
j
20F05 20F10 20F36
right complemented presentations; generators; relations; Artin's braid groups; quadratic algorithms; word problems
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.
S.C.Althoen (Flint)