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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Mathematics
, 2025, Issue 1, pp. 1–10
ISSN Online: 0000-0000
DOI:
10.xxxx/example-doi