Tohoku Mathematical Journal

The rank of the group of relative units of a Galois extension

Yoshitaka Odai and Hiroshi Suzuki

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For an extension of number fields, we define the group of relative units, and determine its rank when the extension is a Galois extension. For this purpose we need to determine all the finite groups of which every abelian subgroup is cyclic.

Article information

Tohoku Math. J. (2), Volume 53, Number 1 (2001), 37-54.

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R27: Units and factorization
Secondary: 11R32: Galois theory 20D99: None of the above, but in this section


Odai, Yoshitaka; Suzuki, Hiroshi. The rank of the group of relative units of a Galois extension. Tohoku Math. J. (2) 53 (2001), no. 1, 37--54. doi:10.2748/tmj/1178207530.

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  • [1] Y. ODAI, On the group of units of an abelian extension of an algebraic number field, Proc. Japan Acad. Ser. A 64 (1988), 304-306.
  • [2] M. SUZUKI, Group theory I, II, Grundlehren Math. Wiss. 247, 248, Springer-Verlag, Berlin-Heidelberg-Ne York, 1982, 1986.