Distributively generated centralizer near-rings

Abstract

Let G G be a finite group. A \mathcal {A} a group of automorphisms of G G and C ( A ; G ) \mathcal {C}\left ( {\mathcal {A};G} \right ) the centralizer near-ring determined by the pair ( A , G ) (\mathcal {A},G) . In this paper we investigate the structure of those centralizer near-rings C ( A ; G ) \mathcal {C}\left ( {\mathcal {A};G} \right ) which are distributively generated. Particular attention is given to the situation in which G G is a solvable group.