ON NONINNER AUTOMORPHISMS OF FINITE NONABELIAN p-GROUPS

A long-standing conjecture asserts that every finite nonabelian p-group has a noninner automorphism of order p. In this paper the verification of the conjecture is reduced to the case of p-groups G satisfying Z(2)*(G) <= C-G(Z(2)*(G)) = Phi(G), where Z(2)*(G) is the preimage of Omega(1)(Z(2)(G)/Z(G)) in G. This improves Deaconescu and Silberberg's reduction of the conjecture: if Z(2)*(G) <= C-G(Z(2)*(G)) = Phi(G), then G has a noninner automorphism of order p leaving the Frattini subgroup ofG elementwise fixed [`Noninner automorphisms of order p of finite p-groups',