Generic and Relations in Monomial Groups Over an Associative Ring (Part I)

Abstract

The question of representing linear groups (and related constructions) by generating elements and defining relations has always been of great interest in general combinatorial group theory. Today, there are a large number of journal and book materials in this direction. Research methods have also emerged. One such method is the (universal) combinatorial method for transforming letters. The essence of this method is to convert the words of the selected alphabet of the group, Monn(R), n≥2, under consideration to their standard forms c 1≠0. The paper gives a description in terms of generators and defining relations of the monomial group defined over an arbitrary associative ring with. Using this result, we find a combinatorial description of also the projective factor PMonn(R)of the named group. When solving these issues, the mentioned method of transformation was used.