Geodesic
The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 2, pp. 81-86.

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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.
Keywords: relatively free groups, nonamenable group, reduced $C^*$-algebra of a group.
Mots-clés : $C^*$-simple group, amenable radical 
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V. S. Atabekyan. The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 2, pp. 81-86. http://geodesic.mathdoc.fr/item/UZERU_2020_54_2_a0/

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