Automorphism Groups of Regular Elements with Von-Neumann Inverses of Local Near-Rings Admitting Frobenius Derivations
Joseph Motanya Abuga
Department of Mathematics, Masinde Muliro University of Science and Technology, Kenya.
Michael Onyango Ojiema *
Department of Mathematics, Masinde Muliro University of Science and Technology, Kenya.
Benard Muthiani Kivunge
Department of Mathematics, Kenyatta University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This paper presents the classication of the invariant subgroups of the automorphism groups of the regular elements obtained from nite 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 pk; k = 1; 2 ; k \(\ge\) 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 elements.
Keywords: Regular elements, von-neumann inverses, zero symmetric local near-rings