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Countable abelian groups with a discrete norm are free


Author: John Lawrence
Journal: Proc. Amer. Math. Soc. 90 (1984), 352-354
MSC: Primary 20K20; Secondary 20K45
DOI: https://doi.org/10.1090/S0002-9939-1984-0728346-9
MathSciNet review: 728346
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Abstract: It is proved that a countable Abelian group with a norm which induces the discrete topology is free.


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

  • [1] László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
  • [2] G. Hardy and E. Wright, An introduction to the theory of numbers, Oxford Univ. Press, 1959.
  • [3] B. H. Neumann and Hanna Neumann, On a class of abelian groups, Arch. Math. (Basel) 4 (1953), 79–85. MR 0055995, https://doi.org/10.1007/BF01899666
  • [4] W. Ralph, Variants of the singular complex and their connections with Banach algebras, Čech cohomology and co-products, Doctoral Thesis, Univ. of Waterloo, 1982.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0728346-9
Keywords: Abelian group, norm
Article copyright: © Copyright 1984 American Mathematical Society