Noninner automorphisms of order \(p\) in finite \(p\)-groups of coclass 2, when \(p>2\). (Q2922935)

The authors show that, for an odd prime \(p\), every \(p\)-group \(G\) of coclass 2 and order \(p^n\) has a noninner automorphism of order \(p\), which fixes either the Frattini subgroup of \(G\), or fixes \(Z_{n-4}(G)\).NEWLINENEWLINE The proof is based on reducing the problem to a precise configuration where a normal subgroup \(N\) of \(G\) has prescribed properties and then two derivations from \(G/N\) to \(N\) are constructed and used to produce two noncentral automorphisms of order \(p\) centralizing both \(N\) and \(G/N\). It is then proved that these two automorphisms cannot be both inner.