Abstract
We are concerned with an algorithm for determining the index (when it is finite) of a subgroup H of a group K when K is specified by a finite set of generators and relations and H is specified as generated by a finite set of words in the generators of K. A systematic computational attack on the problem was discovered by Coxeter and Todd [l], and has proved to be a very useful tool in problems involving generators and relations in groups [2]. Although the method was not completely formalized it was clearly possible to convert it into a computer program, and this has been done by a number of people. Leech has given a survey of this work in [3], where further references may be found.
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