Groups Defined by Rewrite Systems

This is a category of finitely presented groups where the relations are interpreted as rewrite rules. If the group is defined by a confluent system of rewrite rules then we have a normal form for its elements and hence a solution to the word problem. A group belonging to this category is typically constructed by applying the Knuth-Bendix procedure. As in the case of monoids, Magma uses the Knuth-Bendix developed by Derek Holt as part of his package kbmag.

• Construction of an RWS group from an fp-group using the Knuth-Bendix procedure. Orderings supported include: RT-recursive, recursive, ShortLex, WT-ShortLex and Wreath
• Test a rewrite system for confluence
• Reduction of a word to normal form
• Operations on words: Product, exponentiation, inverse, equality
• Enumeration of elements
• Test for a group being finite
• Definition of homomorphisms whose domain or codomain is an RWS group