On central automorphisms of finite p-groups of class 2

Abstract

Let G be a finite p-group and let Aut_c(G) be the group of all central automorphisms of G. Let  be the set of all central automorphisms of G fixing Z(G) elementwise. For a finite p-group of class 2, we have . In [6] we proved  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 , and then we characterize the finite p-groups G satisfying . As a consequence, we prove the main results of Curran and McCaughan [2].