title: ON A GENERALIZATION OF DEHN'S ALGORITHM.
abstract: Viewing Dehn's algorithm as a rewriting system, we generalize to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include finitely generated nilpotent groups, many relatively hyperbolic groups including geometrically finite groups and fundamental groups of certain geometrically decomposable 3-manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm. We dub these Cannon's algorithms.
authors.affiliation: Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia.
authors.forename: Oliver
authors.initials: O
authors.lastname: Goodman
authors.forename: Michael
authors.initials: M
authors.lastname: Shapiro