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Mathematical Notes

, Volume 99, Issue 5–6, pp 631–635 | Cite as

C*-simplicity of n-periodic products

  • S. I. AdyanEmail author
  • V. S. Atabekyan
Article
  • 47 Downloads

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.

Keywords

n-periodic product C*-simple group nonsimple C*-simple groups without free subgroups trivial amenable radical 

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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia
  2. 2.Yerevan State UniversityYerevanArmenia

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