Automorphisms of Finite Groups Inducing Inner Autormorphisms of Integral Group Rings

Let G be a finite group and Z the ring of rational integers.Denote by AutZ(G) the group of all automorphisms of G that induce inner automorphisms of ZG,and let OutZ(G)=AutZ(G)/Inn(G).It is proved that if G admits a direct product decomposition,then AutZ(G) and OutZ(G) also admit direct product decompositions.One of the deducations of the above results is that the normalizer property holds for G if and only if it holds for G1 and G2.The results obtained in this paper execnds the conclasions obtained in [1].