Geodesic
$C^*$-Simplicity of $n$-Periodic Products
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 643-648

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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, nonsimple $C^*$-simple groups without free subgroups, trivial amenable radical.
Mots-clés : $C^*$-simple group 
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     author = {S. I. Adian and V. S. Atabekyan},
     title = {$C^*${-Simplicity} of $n${-Periodic} {Products}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--648},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a0/}
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S. I. Adian; V. S. Atabekyan. $C^*$-Simplicity of $n$-Periodic Products. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 643-648. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a0/