A characteristic of Dedekind groups (Q2721536)

An automorphism \(\alpha\) of a group \(G\) is called a weak power automorphism of \(G\), if \(H\alpha\subseteq H\) for every nonnormal subgroup \(H\) of \(G\). If \(G\) is a finite group with a fixed-point-free weak power automorphism, then \(G\) is a Dedekind group (Theorem 2). This result extends a result by the author and \textit{J. Wang} [Acta Math. Sin. 38, No. 3, 381-385 (1995; Zbl 0831.20024)].