Periodica Mathematica Hungarica

, Volume 69, Issue 1, pp 53–60 | Cite as

A condition of indecomposability for Butler \(\mathrm B (n)\)-groups

  • Clorinda De Vivo
  • Claudia MetelliEmail author


We give a manageable sufficient condition for indecomposability of Butler \(\mathrm B (n)\)-groups, allowing the easy construction of a big family of indecomposable torsionfree Abelian groups of finite rank.


Abelian group Torsionfree Finite rank Butler group B(n)-group  Type Tent 

Mathematics Subject Classification

20K15 06F99 06B99 


  1. 1.
    D.M. Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, CMS Books in Mathematics 2 (Springer, New York, 2000)CrossRefGoogle Scholar
  2. 2.
    M.C.R. Butler, A class of torsion-free abelian groups of finite rank. Proc. Lond. Math. Soc. 15, 680–698 (1965)CrossRefzbMATHGoogle Scholar
  3. 3.
    C. De Vivo, C. Metelli, On direct decompositions of Butler \(B(2)\)-groups, in Volume in Memory of A.L.S. Corner, Contributions to Module Theory; Models, Modules and Abelian Groups, ed. by R. Göbel, B. Goldsmith (W. De Gruyter, New York, 2008), pp. 201–219Google Scholar
  4. 4.
    C. De Vivo, C. Metelli, Butler’s theorem revisited, in Groups and Model Theory, (Contemporary Mathematics, AMS, Providence, 2012) pp. 57–76Google Scholar
  5. 5.
    L. Fuchs, Infinite Abelian Groups, vol. II (Academic Press, London, 1973)zbMATHGoogle Scholar
  6. 6.
    C. De Vivo, C. Metelli, Decomposing \(B(1)\)-groups: an algorithm. Commun. Algebra 30(12), 5621–5637 (2002)CrossRefzbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.NapoliItaly
  2. 2.PadovaItaly

Personalised recommendations