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Groups with a complemented presentation. (English) Zbl 0870.20023
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.

##### 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
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##### References:
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