Automatic Groups

This category corresponds to short-lex automatic groups. A group is represented by four automata: first and second word-difference machines, a word-acceptor, and a multiplier. These automata are constructed using the Knuth-Bendix procedure. This category is implemented by Derek Holt's package kbmag.

• Construction of an automatic group from an fp-group using the Knuth-Bendix procedure.
• Reduction of a word to normal form
• Product, exponentiation, inverse, equality of elements
• Enumeration of words without repetition
• Test for a group being finite
• Growth function for a group
• Definition of homomorphisms whose domain or codomain is an automatic group