THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM

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THE SET OF 2-GENERETED C∗ -SIMPLE RELATIVELY FREE GROUPS HAS THE CARDINALITY OF THE CONTINUUM Varujan Atabekyan

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.

DOI: 10.46991/PYSU:A/2020.54.2.081 Physical and Mathematical Sciences, 54(2 (252) 81-86

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Keywords

relatively free groups, C∗-simple group, amenable radical, non-amenable group, reduced C∗-algebra of a group

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