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    Author(s)

    Hayk Aslanyan, PhD. Amirjan Gevorgyan — Academia (Universities, Colleges and other higher learning entities) (Yerevan State University), PhD. Hayk Grigoryan — Academia (Universities, Colleges and other higher learning entities) (Russian-Armenian University)
    Category: Mathematics
    DOI: 10.52737/18291163-2019.11.6-1-6
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      Finite subgroups of the free groups of the infinitely based varieties of S.I. Adian

      Hayk Aslanyan, PhD. Amirjan Gevorgyan — Academia (Universities, Colleges and other higher learning entities) (Yerevan State University), PhD. Hayk Grigoryan — Academia (Universities, Colleges and other higher learning entities) (Russian-Armenian University)
      This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

      Submitted: 2024-12-10; Published: 2022-09-15
      © 2025 by author(s) and The Gufo Inc.
      CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

      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 mm in this varieties is of continuum cardinality for every finite rank m>1m>1.

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