Splitting length of abelian mixed groups of torsion-free rank 1

  • Pham Thi Thu Thuy


The splitting length of a mixed Abelian group G is defined as the smallest positive integer n such that \( \mathop \otimes \limits^n G \) splits. The task of determining the splitting length of mixed Abelian groups was formulated by Irwin, Khabbaz, and Rayna. In this paper, a criterion for determining whether \( \mathop \otimes \limits^n G \) splits for countable mixed Abelian groups G of torsion-free rank 1 is found.


Abelian Group Prime Number Direct Summand Ordinal Number Mixed Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    L. Fuchs, “Notes on Abelian groups. I, II,” Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 2, 5–23 (1959); Acta Math. Acad. Sci. Hungar., 11, 117–125 (1960).MATHGoogle Scholar
  2. 2.
    L. Fuchs, Infinite Abelian Groups, Academic Press, New York (1970).MATHGoogle Scholar
  3. 3.
    J. M. Irwin, S. A. Khabbaz, and G. Rayna, “The role of the tensor product in the splitting of Abelian groups,” J. Algebra, 14, 423–422 (1970).MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    L. Kulikov, “On the theory of Abelian groups of arbitrary power,” Mat. Sb., 9, 165–182 (1941).MATHGoogle Scholar
  5. 5.
    D. A. Lawver and E. H. Toubassi, “Tensor products and the splitting of Abelian groups,” Can. J. Math., 23, No. 5, 764–770 (1971).MATHMathSciNetGoogle Scholar
  6. 6.
    C. Megibben, “On mixed groups of torsion-free rank one,” Illinois J. Math., 11, 134–144 (1967).MATHMathSciNetGoogle Scholar
  7. 7.
    J. Rotman, “Torsion-free and mixed Abelian groups,” Illinois J. Math., 5, 131–143 (1961).MATHMathSciNetGoogle Scholar
  8. 8.
    E. H. Toubassi and D. A. Lawver, “Height-slope and splitting length of Abelian groups,” Publ. Math. Debrecen, 20, 63–71 (1973).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

Personalised recommendations