Journal of Mathematical Sciences

, Volume 197, Issue 5, pp 635–648 | Cite as

Warfield’s Duality and Malcev’s Matrix

  • J. V. Kostromina


In this work, we investigate relations between Malcev’s matrices of a torsion-free group G of finite rank and Malcev’s matrices of groups Hom(R,G) and Hom(G,R), where G is a locally free group and R is a torsion-free group of rank 1.


Abelian Group Prime Number Residue Class Normal Matrice Isomorphic 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. M. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., V. 931, Springer, Berlin (1982).Google Scholar
  2. 2.
    D. Derry, “Über eine Klasse von Abelschen Gruppen,” Proc. London Math. Soc., 43, 490–506 (1938).CrossRefMathSciNetGoogle Scholar
  3. 3.
    A. A. Fomin, “Invariants for Abelian groups and dual exact sequences,” J. Algebra, 322, 2544–2565 (2009).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    L. Fuchs, Infinite Abelian Groups, Academic Press, New York (1970, 1973).Google Scholar
  5. 5.
    A. G. Kurosh, “Primitive torsionfreie abelsche Gruppen vom endlichen Range,” Ann. Math., 38, 175–203 (1937).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    A. G. Kurosh, Theory of Groups [in Russian], Moscow (1967).Google Scholar
  7. 7.
    A. I. Malcev, “Torsion-free Abelian group of finite rank,” Math. J., 4, 45–68 (1938).MATHGoogle Scholar
  8. 8.
    R. B. Warfield, Jr., “Homomorphisms and duality for Abelian groups,” Math. Z., 107, 189–212 (1968).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Moscow Pedagogical State UniversityMoscowRussia

Personalised recommendations