Some necessary and sufficient conditions on commuting automorphisms of some finite p-groups

Abstract

Let G be a finite non-abelian p-group of order greater than p 4, p an odd prime, such that is cyclic and Z(H) is elementary abelian, where We prove that the set of all commuting automorphisms of G forms a subgroup of if and only if is abelian. Also, we find the structure of for a finite 2-group G of almost maximal class with cyclic center Z(G), where denotes the set of all central automorphisms of G.