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Proceedings of the American Mathematical Society

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On type sets of torsion-free abelian groups of rank 2


Author: Ryuichi Ito
Journal: Proc. Amer. Math. Soc. 48 (1975), 39-42
DOI: https://doi.org/10.1090/S0002-9939-1975-0354900-7
MathSciNet review: 0354900
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Abstract | References | Additional Information

Abstract: We prove existence of a torsion-free abelian group with a prescribed type-set.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Beaumont and R. S. Pierce, Torsion free groups of rank two, Mem. Amer. Math. Soc. No. 38 (1961), 41. MR 0130297
  • [2] L. Fuchs, Infinite abelian groups. Vols. I, II, Pure and Appl. Math., vol. 36, Academic Press, New York, 1970, 1973. MR 41 #333.
  • [3] John Koehler, Some torsion-free rank two groups, Acta Sci. Math. (Szeged) 25 (1964), 186–190. MR 0169909
  • [4] John E. Koehler, The type set of a torsion-free group of finite rank, Illinois J. Math. 9 (1965), 66–86. MR 0171841
  • [5] A. E. Ingham, The distribution of prime numbers, Cambridge Tracts in Mathematics and Mathematical Physics, No. 30, Stechert-Hafner, Inc., New York, 1964. MR 0184920


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0354900-7
Keywords: Type, type-set, characteristic, completely anisotropic, relatively disjoint
Article copyright: © Copyright 1975 American Mathematical Society