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

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