Skip to main content

Local Abelian Torsion-Free Groups


A representation for p-local Abelian torsion-free groups of finite rank is obtained in terms of homomorphisms of p-adic modules of finite rank with fixed basis.

This is a preview of subscription content, access via your institution.


  1. 1.

    V. Kh. Farukshin, Endomorphisms of Reduced Generally Primary Torsion-Free Groups [in Russian], Abstract of Ph.D. Thesis, Moscow (1986).

  2. 2.

    A. A. Fomin, “Some mixed Abelian groups as modules over the ring of pseudo-rational numbers,” in: Abelian Groups and Modules. Trends in Mathematics, Birkhäuser, Basel (1999), pp. 87–100.

  3. 3.

    A. A. Fomin, “Quotient divisible mixed groups,” in: Abelian Groups, Rings and Modules, Contemp. Math., Vol. 273, Amer. Math. Soc. (2001), pp. 117–128.

  4. 4.

    L. Fuchs, Infinite Abelian Groups, Vols. 1, 2 [Russian translation], Mir, Moscow, 1974, 1977.

  5. 5.

    P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Abelian Groups and Its Rings of Endomorphisms [in Russian], Tomsk (2002).

  6. 6.

    C. Murley, “Classification of certain classes of Abelian torsion-free groups,” Pacific J. Math., 40, 647–665 (1972).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to V. Kh. Farukshin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 147–152, 2011/12.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Farukshin, V.K. Local Abelian Torsion-Free Groups. J Math Sci 197, 684–687 (2014).

Download citation


  • Abelian Group
  • Independent System
  • Finite Rank
  • Discrete Valuation Ring
  • Independent Modulo