On a generalization of Dehn's algorithm

Details On a generalization of Dehn's algorithm On a generalization of Dehn's algorithm

2007-06-20

arxiv.org/abs/0706.3024v4

Mathematics

Group Theory

33 pages, 2 figures, credits Kambites and Otto, mentions new work in progress

Scientific paper

Viewing Dehn's algorithm as a rewriting system, we generalise 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 nilpotent groups, many relatively hyperbolic groups including geometrically finite groups and fundamental groups of certain geometrically decomposable 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.

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