Constructing Matrix Representations of Finitely Presented Groups

The Todd-Coxeter coset enumeration algorithm is one of the most powerful tools of computational group theory. It may be viewed as a means of constructing permutation representations of nitely presented groups. In this paper we present an analogous algorithm for directly constructing matrix representations over many elds. In fact the algorithm is more general than this, and can be used to construct matrix representations of nitely generated algebras. The algorithm (with some restrictions) has been implemented as a C program and some results obtained with this implementation are described.