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Proceedings of the YSU, Physical and Mathematical Sciences, 2020, Volume 54, Issue 2, Pages 81–86
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Mathematics
The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum
V. S. Atabekyan
Yerevan State University, Faculty of Mathematics and Mechanics
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.
Keywords:
relatively free groups, $C^*$-simple group, amenable radical, nonamenable group, reduced $C^*$-algebra of a group
DOI:
https://doi.org/10.46991/PYSU:A/2020.54.2.081
 Full text:
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MSC: Primary 20F05; Secondary 20E10, 20E05, 20D45
Received: 04.08.2020
Revised: 14.08.2020
Accepted:17.08.2020
Language:
Citation:
V. S. Atabekyan, “The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum”, Proceedings of the YSU, Physical and Mathematical Sciences, 54:2 (2020), 81–86
Citation in format AMSBIB
\Bibitem{Ata20}
\by V.~S.~Atabekyan
\paper The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2020
\vol 54
\issue 2
\pages 81--86
\mathnet{http://mi.mathnet.ru/uzeru708}
\crossref{https://doi.org/10.46991/PYSU:A/2020.54.2.081}
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http://mi.mathnet.ru/eng/uzeru708 http://mi.mathnet.ru/eng/uzeru/v54/i2/p81
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