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

Sh.A. Stepanyan

doi:10.46991/PYSU:A/2017.51.2.196

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

Authors

Sh.A. Stepanyan Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2017.51.2.196

Keywords:

relatively free group, automorphism, periodic group

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.

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Published

2017-06-15

How to Cite

Stepanyan, S. (2017). ON AUTOMORPHISMS OF THE RELATIVELY FREE GROUPS SATISFYING THE IDENTITY $[x^n; y] = 1$. Proceedings of the YSU A: Physical and Mathematical Sciences, 51(2 (243), 196–198. https://doi.org/10.46991/PYSU:A/2017.51.2.196