The automorphism group of a nonsplit metacyclic \(p\)-group. (Q933728)

The author considers a finite group \(G=HK\), where \(K\triangleleft G\) and \(H\leqslant G\). Theorem 2.1 is a relevant technical result which produces several subgroups of \(\Aut(G)\) arising from special automorphisms of \(H\), crossed homomorphisms from \(H\) to \(Z(K)\) etc. Theorem 2.1 is then used in the sequel to attack the special case when \(G\) is a nonsplit metacyclic \(p\)-group (\(p>2\)) and obtain (Theorem 3.5) a decomposition of \(\Aut(G)\) as a product of three special subgroups.