Tohoku Mathematical Journal
2001
March
SECOND SERIES VOL. 53, NO. 1

Tohoku Math. J.
53 (2001), 37-54

Title THE RANK OF THE GROUP OF RELATIVE UNITS OF A GALOIS EXTENSION

Author Yoshitaka Odai and Hiroshi Suzuki

(Received November 27, 1998, revised July 10, 2000)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 11R27; Secondary 20D99.

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