10.59 (1986)

Is a $p'$-group $G$ locally nilpotent if it admits a splitting automorphism $\varphi$ of prime order $p$ such that all subgroups of the form $\langle g, g^\varphi, \dots, g^{\varphi^{p-1}} \rangle$ are nilpotent? An automorphism $\varphi$ of order $p$ is called splitting if $g g^\varphi g^{\varphi^2} \dots g^{\varphi^{p-1}} = 1$ for all $g \in G$.