STUDY THE NIL-POTENT SUBGROUPS OF CLASSICAL GROUPS OVERLAPPING WITH COMMUNICATION RINGS

Abstract

Let there be an infinite division ring, which will be denoted by the letter D, let there be a natural number, which will be denoted by the letter n, and let there be a subnormal subgroup of GL_n(D), which will be denoted by the letter N, “such that either n = 1 or the centre of D includes at least five different elements”. We give proof that locally nilpotent linear groups are divisible by residually-periodic, and we show that these groups actually benefit from a broad variety of increased characteristics. In addition, we present evidence that locally nilpotent linear groups are divisible by residually-periodic. The use of examples places significant limitations on the scope of possible extensions; however, we do expand the scope of our findings beyond linear groups to groups of automorphisms of both Noetherian modules and Artinian modules over commutative rings. This brings the total number of possible extensions down to a much more manageable level. In conclusion, we have shown that two fascinating theorems concerning nilpotent subgroups may be proven satisfactorily