Adjoint groups of $p$-nil rings and $p$-group automorphisms

Abstract

We introduce a class of rings, namely the class of left or right $p$-nil rings, for which the adjoint groups behave regularly. Every $p$-ring is close to being left or right $p$-nil in the sense that it contains a large ideal belonging to this class. Also their adjoint groups occur naturally as groups of automorphisms of $p$-groups. These facts and some of their applications are investigated in this paper.

arXiv commentSome of the results proved by the authors in "On Central Automorphisms of Groups And Nilpotent Rings", are included in this paper