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Convergent Sequences in Discrete Groups

  Published:2011-08-03
 Printed: Jun 2013
  • Andreas Thom,
    UniversitÀt Leipzig, Germany
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Abstract

We prove that a finitely generated group contains a sequence of non-trivial elements that converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian. As a consequence of the methods used, we show that a finitely generated group satisfies Chu duality if and only if it is virtually abelian.
Keywords: Chu duality, Bohr topology Chu duality, Bohr topology
MSC Classifications: 54H11 show english descriptions Topological groups [See also 22A05] 54H11 - Topological groups [See also 22A05]
 

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