ON CENTRAL AUTOMORPHISMS OF FINITE p-GROUPS OF CLASS 2

Let G be a finite p-group and let Aut(c)(G) be the group of all central automorphisms of G. Let C-Autc(G)(Z(G)) be the set of all central automorphisms of G fixing Z(G) elementwise. For a finite p-group of class 2, we have Inn(G) <= C-Autc (G)(Z(G)). In [6] we proved C-Autc(G) (Z(G)) = Inn(G) if and only if Z(G) is cyclic. In this paper we first prove that there is no finite p-group of class 2 for which [C-Autc(G) (Z(G)) : Inn(G)] = p, and then we characterize the finite p-groups G satisfying [C-Autc(G) (Z(G)) : Inn(G)] = p(2). As a consequence, we prove the main results of Curran and McCaughan [2].