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Periodica Mathematica Hungarica

, Volume 69, Issue 1, pp 21–31 | Cite as

The Hopfian exponent of an abelian group

  • Brendan GoldsmithEmail author
  • Peter Vámos
Article

Abstract

If \(G\) is a Hopfian abelian group then it is, in general, difficult to determine if direct sums of copies of \(G\) will remain Hopfian. We exhibit large classes of Hopfian groups such that every finite direct sum of copies of the group is Hopfian. We also show that for any integer \(n > 1\) there is a torsion-free Hopfian group \(G\) having the property that the direct sum of \(n\) copies of \(G\) is not Hopfian but the direct sum of any lesser number of copies is Hopfian.

Keywords

Abelian groups Hopfian groups Leavitt rings 

Mathematics Subject Classification

Primary 20K30 Secondary 20K20 20K10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesDublin Institute of TechnologyDublin 8Ireland
  2. 2.Department of MathematicsUniversity of ExeterExeterUK

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