Representations, commutative algebra, and Hurwitz groups

Characteristic zero representations of the (2,3,7)-triangle group in degrees up to seven are constructed by using Janet's algorithm for solving polynomial equations. These are used to find families of Hurwitz groups, i.e. finite epimorphic images. For some varieties of representations it is investigated whether additional relations can be uniformly imposed and still result in subvarieties of representations. The methods are of more general interest. Some remarks about the interaction of positive characteristics and characteristic zero are made.