Confluent string rewriting
String-rewriting systems
A finiteness condition for rewriting systems
Theoretical Computer Science
Word Processing in Groups
On properties not inherited by monoids from their Schützenberger groups
Information and Computation
Homotopy bases and finite derivation type for Schützenberger groups of monoids
Journal of Symbolic Computation
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Results of Anick (1986), Squier (1987), Kobayashi (1990), Brown (1992b), and others, show that a monoid with a finite convergent rewriting system satisfies a homological condition known as FP∞.In this paper we give a simplified version of Brown's proof, which is conceptual, in contrast with the other proofs, which are computational.We also collect together a large number of results and examples of monoids and groups that satisfy FP ∞ and others that do not. These may provide techniques for showing that various monoids do not have finite convergent rewriting systems, as well as explicit examples with which methods can be tested.