Automorphisms of \(p\)-groups of maximal class. (Q2504989)

Summary: \textit{A. Juhász} [Trans. Am. Math. Soc. 270, 469-481 (1982; Zbl 0488.20023)] has proved that the automorphism group of a group \(G\) of maximal class of order \(p^n\), with \(p\geq 5\) and \(n>p+1\), has order divisible by \(p^{\lceil(3n-2p+5)/2\rceil}\). We show that by translating the problem in terms of derivations, the result can be deduced from the case where \(G\) is metabelian. Here one can use a general result of \textit{A. Caranti} and \textit{C. M. Scoppola} [Arch. Math. 56, No. 3, 218-227 (1991; Zbl 0693.20038)] concerning automorphisms of two-generator, nilpotent metabelian groups.