Natural Science, Physics, 2025
ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPSSATISFYING THE IDENTITY [xn,y] =1
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Submitted: 2025-02-06; Published: 2025-02-06
© 2025 by author(s) and The Gufo Inc.
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Abstract
We prove that if an automorphism j of the relatively free group of the group variety, defined by the identity relation [xn;y]=1, acts identically on its center, then j has either infinite or odd order, where n≥665 is an arbitrary odd number.