Coset enumeration on digital computers

Abstract

In 1936 Todd and Coxeter gave a method ((10), also described in (4), ch. 2) for establishing the order of a finite group defined by a set of relationssatisfied by its generators S1, S2,…, Sk. They enumerate systematically the cosets of a suitable subgroup whose order is evident from the defining relations for the whole group. They describe the method as being ‘purely mechanical’, and since that date the advent of electronic computers has led a number of people to programme the method for automatic execution. Most of this work has remained unpublished; an account is given here of work known to the author.