The centralizer of the general linear group

Abstract

Let G be a group, written additively with identity 0, but not necessarily abelian and let S be a semigroup of endomorphisms of G. The set for all is a zero-symmetric near-ring with identity under the operations of function addition and composition, called the centralizer near-ring determined by the pair (S, G). Centralizer near-rings are general, for if N is any zero-symmetric near-ring with identity then there exists a group G and a semigroup S⊇ G such that For background material and definitions relative to near-rings in general we refer the reader to the book by Pilz [7]. For material on centralizer near-rings we refer the reader to [4] and [6].