SCIENCE & INNOVATION

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

01.11.2023 International Scientific Journal "Science and Innovation". Series A. Volume 2 Issue 10

Satarov Zhoomart, Mamaziaeva Elmira, Mambetov Zhoomart, Orunbaeva N.A

Abstract. This work continues the research begun in its first part, where generalized m-triangular groups over an arbitrary associative ring R were studied from the standpoint of generators and relations. The named generators and relations were identified there uniformly for all values of m. A combinatorial description of the projective factors of the named groups was also found there. In combinatorial theory, descriptions of not only some classical subgroups of a complete linear group, but also their natural parts are of interest. In this part of the work, the generators and defining relations of the generalized elementary triangular group and its projective factor are similarly identified over an arbitrary associative ring R.

Keywords: commutator, alphabet, standard forms, generators, relations, transformational transformations, completeness of relations, center