ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPS SATISFYING THE IDENTITY $[x^n; y] = 1$

Abstract

We prove that if an automorphism j of the relatively free group of the group variety, defined by the identity relation $[x^n; y] = 1$, acts identically on its center, then j has either infinite or odd order, where $n\geq 665$ is an arbitrary odd number.