Experiments in Coset Enumeration

Coset enumeration, based on the methods described by Todd and Coxeter, is one of the most important tools for investigating nitely presented groups. Such methods do not, in general, constitute an algorithm. Each problem has to be addressed individually, and determining whether or not an acceptable solution for a diicult problem can be found using given resources requires an empirical approach (i.e., experimentation). We discuss some of the ideas involved, and illustrate with examples which emphasize some of the possibilities.