Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian

Hayk T. Aslanyan; Amirjan L. Gevorgyan; Hayk A. Grigoryan

doi:10.52737/18291163-2019.11.6-1-6

Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian

Authors

Hayk T. Aslanyan American University of Armenia
Amirjan L. Gevorgyan Yerevan State University
Hayk A. Grigoryan Russian-Armenian University

DOI:

https://doi.org/10.52737/18291163-2019.11.6-1-6

Keywords:

infinitely based variety, torsion-free groups, free Burnside group

Abstract

It is proved that all finite subgroups of the free groups of the infinitely based varieties of S.I. Adian are cyclic. The set of all non-isomorphic free groups of rank $m$ in this varieties is of continuum cardinality for every finite rank $m > 1$.

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Published

2019-05-08 — Updated on 2022-09-15

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2022-09-15 (2)
2019-05-08 (1)

Issue

Vol. 11 No. 6 (2019): Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian

Section

Articles

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]

H. T. Aslanyan, A. L. Gevorgyan, and H. A. Grigoryan, “Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian”, Armen.J.Math., vol. 11, no. 6, pp. 1–6, Sep. 2022, doi: 10.52737/18291163-2019.11.6-1-6.