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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.

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