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Journal of Mathematical Sciences

, Volume 154, Issue 3, pp 422–429 | Cite as

On subdirect sums of Abelian torsion-free groups of rank 1

  • V. B. Trukhmanov
Article
  • 15 Downloads

Abstract

In this paper, we study torsion-free Abelian groups of rank 2, which are subdirect sums of two divisible rational groups, with the inducing group ℚ/ℤ. The class of special groups is defined and investigated. It is shown that there is a one-to-one correspondence between the set of all special groups and the multiplicative group of unity elements of the ring of universal numbers.

Keywords

Abelian Group Basic Element Special Group Characteristic Sequence Multiplicative Group 
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References

  1. 1.
    L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, New York (1970).MATHGoogle Scholar
  2. 2.
    L. Kulikov, “Subdirect decompositions of countable Abelian torsion-free groups,” in: Xth All-Union Algebraic Colloquium, Novosibirsk (1969), pp. 18–19.Google Scholar
  3. 3.
    L. Kulikov, “On subdirect sums of Abelian torsion-free groups of rank 1,” XIIth All-Union Algebraic Colloquium, Sverdlovsk (1973), p. 30.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Arzamas State Pedagogical InstituteArzamas, Nizhegorodskaya RegionRussia

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