Automorphism Groups of Regular Elements with Von-Neumann Inverses of Local Near-Rings Admitting Frobenius Derivations

Abstract

This paper presents the classification of the invariant subgroups of the automorphism groups of the regular elements obtained from finite local near-rings, the appropriate algebraic structure to study non-linear functions on finite groups. Just as rings of matrices operate on vector spaces, near-rings operate on groups. In this paper, we construct classes of zero symmetric local near-ring of characteristic p k ; k = 1, 2 , k ≥ 3 admitting frobenius derivations, characterize the structures of the cyclic groups generated by the regular elements R(N ) as well as the structures and the orders of the automorphism groups Aut(R(N )) of the regular element