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 ≥ 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.
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Original Russian Text © S. I. Adyan, V. S. Atabekyan, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 5, pp. 643–648.
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Adyan, S.I., Atabekyan, V.S. C*-simplicity of n-periodic products. Math Notes 99, 631–635 (2016). https://doi.org/10.1134/S0001434616050011
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DOI: https://doi.org/10.1134/S0001434616050011