2020; Physical and Mathematical Sciences, 54(2 (252): 81–86
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THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

Varujan Atabekyan*

Received: 2025-01-29 · Published: 2020-08-17

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Original title
THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM
Author
Varujan Atabekyan
Published
2020-08-17
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2020.54.2.081

Abstract

In this paper we prove that the set of non-isomorphic 2-generated C∗-simple relatively free groups has the cardinality of the continuum. A non-trivial identity is satisfied in any (not absolutely free) relatively free group. Hence, they cannot contain a non-abelian absolutely free subgroups. The question of the existence of C∗-simple groups without free subgroups of rank 2 was posed by de la Harpe in 2007.
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