GENERATORS AND RELATIONSHIPS IN GENERALIZED M-TRIANGULAR GROUPS OVER AN ASSOCIATE RING. I

The question of representing linear groups (and related constructions) by generating elements and defining relations has always been of interest in general combinatorial group theory. Today, a large amount of magazine and book materials have already accumulated in this direction. New research methods also emerged. One of them is the universal combinatorial transformation method, the essence of which is to transform words of the selected generative alphabet of the group under study to their standard forms. The paper provides a description through generators and defining relations of generalized m-triangular groups  defined over an arbitrary non-zero associative ring. Based on this result, combinatorial descriptions of the projective factors of the named groups  are also found. The solution to these problems is based on the mentioned transformation method.