On automorphism groups of finite \(p\)-groups
It is proved that, for every odd prime number \(p\) and for each \(n \geq 7\), there exists a \(p\)-group \(G\) of order \(p^ n\) such that \(\text{Aut }G = \text{Aut}_ cG \cdot \text{Inn }G\), where \(\text{Aut}_ cG\) denotes the group of all central automorphisms of \(G\). Moreover, it is shown that the \(p\)-groups \(G\) of minimal order with \(\text{Aut }G = \text{Aut}_ cG \cdot \text{Inn }G\) have order \(p^ 6\) and nilpotency class 3. This answers a question of A. Caranti.
scientific article; zbMATH DE number 627434