(untitled) (Communications in Mathematical Research, 2021)
Let G be a finitely generated torsion-free nilpotent group and α an automorphism of prime order p of G. If the map φ : G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h(p), where h(p) is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.