On the Quotient Groups of Subgroups of the Unit Groups of a Class of Completely Primary Finite Rings

Abstract

The study of completely primary finite rings has generated interest ing results in the structure theory of finite rings with identity. It has been shown that a finite ring can be classified by studying the structures of its group of units. But this group has subgroups which are interesting objects of study. Let R be a completely primary finite ring of character istic p n and J be its Jacobson radical satisfying the condition J n = (0) and J n−1 6= (0). In this paper, we characterize the quotient groups of subgroups of the group of units of R.