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

Abstract

This work is a continuation of the first part of the same name. In the first part, the monomial group Monn(R), n≥2 and its projective factor PMonn(R) over an arbitrary basic associative ring R, 1≠0. Were studied from the position of generators and defining relations. Here, a similar problem is solved for elementary monomial groups EMonn(R) and PMonn(R) also over an arbitrary associative ring R. Despite the apparent (external) proximity, monomial and elementary monomial groups turn out to be qualitatively different objects. When solving both of these issues, the combinatorial method of transformation was applied. Unlike monomial groups EMonn(R), the case in when n=2 will be non-traditional. It requires specific and more subtle reasoning.