THE SET OF 2-GENERETED $C^*$-SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

V.S. Atabekyan

doi:10.46991/PYSU:A/2020.54.2.081

THE SET OF 2-GENERETED $C^*$-SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

Authors

V.S. Atabekyan Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2020.54.2.081

Keywords:

relatively free groups, $C^*$-simple group, amenable radical, non-amenable group, reduced $C^*$-algebra of a group

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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Published

2020-08-17

How to Cite

Atabekyan, V. (2020). THE SET OF 2-GENERETED $C^*$-SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM. Proceedings of the YSU A: Physical and Mathematical Sciences, 54(2 (252), 81–86. https://doi.org/10.46991/PYSU:A/2020.54.2.081