2017; Physical and Mathematical Sciences, 51(2 (243): 196–198
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ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPSSATISFYING THE IDENTITY [xn,y] =1

Shogh Stepanyan*

Received: 2025-02-06 · Published: 2017-06-15

© 2017 The Author(s) and the original publisher.

CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPSSATISFYING THE IDENTITY [xn,y] =1
Author
Shogh Stepanyan
Published
2017-06-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2017.51.2.196

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.
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