THE SET OF 2-GENERETED C^*-SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM - Atabekyan, V.S. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2020)
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.