Abstract
Possibly the most frequently used algorithm in computational group theory is the Todd-Coxeter process for enumerating the cosets of a subgroup of a finitely presented group. In all implementations the power of this algorithm is limited much more by its storage requirements than by its execution time. This note outlines a technique which can often be used to economise on storage at the expense of an increased execution time. Before giving details it will be helpful to review some background.
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