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Mat. Zametki, 2016, Volume 99, Issue 5, Pages 643–648 (Mi mz11137)  

This article is cited in 2 scientific papers (total in 2 papers)

$C^*$-Simplicity of $n$-Periodic Products

S. I. Adiana, V. S. Atabekyanb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Yerevan State University

Abstract: The $C^*$-simplicity of $n$-periodic products is proved for a large class of groups. In particular, the $n$-periodic products of any finite or cyclic groups (including the free Burnside groups) are $C^*$-simple. Continuum-many nonisomorphic 3-generated nonsimple $C^*$-simple groups are constructed in each of which the identity $x^n=1$ holds, where $n\ge 1003$ is any odd number. The problem of the existence of $C^*$-simple groups without free subgroups of rank 2 was posed by de la Harpe in 2007.

Keywords: $n$-periodic product, $C^*$-simple group, nonsimple $C^*$-simple groups without free subgroups, trivial amenable radical.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-51-05012
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 15RF-054
15T-1A258
This work was supported by the Russian Foundation for Basic Research of the Russian Federation and the State Science Committee of the Ministry of Education and Science of Republic Armenia in the framework of joint scientific programs nos. 15-51-05012 and 15RF-054, respectively, and by the State Science Committee of the Ministry of Education and Science of the Republic of Armenia in the framework of scientific grant no. 15T-1A258.


DOI: https://doi.org/10.4213/mzm11137

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English version:
Mathematical Notes, 2016, 99:5, 631–635

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 18.11.2015

Citation: S. I. Adian, V. S. Atabekyan, “$C^*$-Simplicity of $n$-Periodic Products”, Mat. Zametki, 99:5 (2016), 643–648; Math. Notes, 99:5 (2016), 631–635

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. I. Adian, V. S. Atabekyan, “Periodic products of groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:3 (2017), 111–117  crossref  mathscinet  zmath  isi  scopus
    2. V. S. Atabekyan, A. L. Gevorgyan, Sh. A. Stepanyan, “The unique trace property of n-periodic product of groups”, J. Contemp. Math. Anal.-Armen. Aca., 52:4 (2017), 161–165  crossref  mathscinet  zmath  isi  scopus
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