Logged Rewriting Procedures with Application to Identities Among Relations

The key idea is that rewriting procedures can be enhanced so that they not only rewrite words but record (log) how the rewriting has taken place. We introduce logged rewrite systems and present a variation on the Knuth-Bendix algorithm for obtaining (where possible) complete logged rewrite systems. This procedure is then applied to work of Brown and Razak Salleh, and an algorithm is developed which provides a set of generators for the module of identities among relations of a group presentation.