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# Convergent Sequences in Discrete Groups

Published:2011-08-03
Printed: Jun 2013
• Andreas Thom,
Universität 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