Commuting Automorphisms Of Finite P-groups

Let G be a group.An automorphism a of G is called a commuting automorphism if[x,xα]=1 for all x ∈ G.The set of all commuting automorphisms of G is denoted by A(G).A group G is called A(G)-group if A(G)forms a subgroup of Aut(G).In this paper we show that G are A(G)-groups for all A1-groups,A2-groups and C2-groups with odd order.In addition,some non-A(G)groups and other results are also given.