Autocentralizer automorphisms of groups

Abstract

Let G be a group and CG(a) be a normal centralizer subgroup of G for some a ∈ G. Assume that, Υa 2(G) = [G, CG(a)] and AutΥa 2 (G) Z(CG(a))(G) is the set of all automorphisms of G that centralizes G Υa 2 (G) and Z(CG(a)). In this paper, we focus on the group AutΥa 2 (G) Z(CG(a))(G) and try to characterize its properties.