An automorphism \(\sigma\) of a group \(G\) is said to be central if, for all \(g\in G\), one has \(\sigma(g)=gz_g\) for some \(z_g\in Z(G)\). Let \(\operatorname{Aut}_c(G)\) denote the group of central automorphisms of \(G\); then \(\operatorname{Aut}_c(G)\) is the centralizer of \(\text{Inn}(G)\) in \(\operatorname{Aut}(G)\). Obviously, if \(\operatorname{Aut}(G)\) is Abelian, then all automorphisms of \(G\) are central. G. A. Miller was the first who presented a nonabelian finite group \(G\) with Abelian \(\operatorname{Aut}(G)\). A group \(G\) is said to be a PN group, if it has no nonidentity Abelian direct factor. Theorem 4.1 yields a necessary and sufficient condition for a finite \(p\)-group \(G\) to have Abelian \(\operatorname{Aut}_c(G)\).