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A Basis Theorem for Subgroups of Bounded Abelian Groups

  • K. Benabdallah
  • S. A. Khabbaz
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 287)

Abstract

In this paper we present a generalization of the main aspects of the basis theorem for pairs (G,H) in which H is a subgroup of a finite abelian group G, see [4], to the case in which G is an abelian group of bounded order. The proof we outline here is actually simpler than the one sketched in [4]. We remark that the assumption of the well ordering principle which occurs in the statement of the theorem is not an essential feature of it.

Keywords

Abelian Group Induction Hypothesis Basis Element Direct Summand Basis Theorem 
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Bibliography

  1. 1.
    Donna Beers, R. Hunter, and E. Walker, Finite Valued p-Groups, Abelian Group Theory, Lecture Notes in Mathematics 1006, Springer-Verlag, New York 1983.Google Scholar
  2. 2.
    S. D. Berman and Z. P. Zilinskaza, On simultaneous direct decompositions of a finitely generated abelian group and a subgroup, translated in Sov. Math. Dokl. 14(1973), pp. 833–837.MATHGoogle Scholar
  3. 3.
    Laszlo Fuchs, Infinite. Abelian Groups, vol. 1, Academic Press New York and London, 1970.Google Scholar
  4. 4.
    S. A. Khabbaz and G. Rayna, A Basis Theorem for Subgroups of Finite Abelian Groups, Abelian Group Theory, Lecture Notes in Mathematics 1006, Springer-Verlag, New York 1983.Google Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • K. Benabdallah
    • 1
  • S. A. Khabbaz
    • 2
  1. 1.Université de MontréalCanada
  2. 2.Lehigh UniversityUSA

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