Generators and relations in generalized m-triangular groups over an associative ring. I

The question of representing linear groups (and related constructions) by forming elements and defining relations has always been of interest in the general combinatorial theory of groups. A large number of magazine and book materials have already accumulated in this direction. New research methods have also emerged. One of them is a universal combinatorial transformation method, the essence of which is to transform the words of the selected generating alphabet of the studied group to their standard forms. The paper describes the generative and defining relations of generalized m-triangular groups defined over an arbitrary nonzero associative ring. Based on this result, combinatorial descriptions of the projective factors of these groups are also found. The mentioned transformation method is used as the basis for solving these tasks.