An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and numerical an with $d = 1$. A growing body recent work examines shifted families semigroups, that is, semigroups the form $M_n \langle n + r_1, \ldots, r_k \rangle$ for fixed $r_1, r_k$, one each value shift parameter $n$. It has been shown within any family size minimal presentation bounded (in fact, thi...

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 constr...

This document contains an ampliied version of the ve talks given by the author at the 22nd Holiday Mathematics Symposium at the New Mexico State University, January 3-7 1997, on the topic \Rewriting Techniques and Non-commutative Grr obner Bases".

One idea how to prove that a finitely presented group G is infinite is to construct suitable homomorphisms into infinite matrix groups. In [HoP 92] this is done by starting with a finite image H of G and solving linear equations to check whether the epimorphism onto H can be lifted to a representation whose image is an extension of a ZZ-lattice by H, thus exhibiting an infinite abelian section ...