Geodesic rewriting systems and pregroups

Details Geodesic rewriting systems and pregroups Geodesic rewriting systems and pregroups

2009-06-11

arxiv.org/abs/0906.2223v1

Mathematics

Group Theory

44 pages, to appear in "Combinatorial and Geometric Group Theory, Dortmund and Carleton Conferences". Series: Trends in Mathem

Scientific paper

In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent and then systems in which the length reducing rules lead to geodesics. Combining these properties we arrive at our main object of study which we call geodesically perfect rewriting systems. We show that these are well-behaved and convenient to use, and give several examples of classes of groups for which they can be constructed from natural presentations. We describe a Knuth-Bendix completion process to construct such systems, show how they may be found with the help of Stallings' pregroups and conversely may be used to construct such pregroups.

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