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On Unit Groups of Absolute Abelian Number Fields of Degree pq

Published online by Cambridge University Press:  22 January 2016

Hideo Yokoi
Hideo Yokoi*
Affiliation:
Mathematical Institute, Nagoya University
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In this note, we denote by Q the rational number field, by EΩ the whole unit group of an arbitrary number field Ω of finite degree, and by rΩ the rank of where generally G* for an arbitrary abelian group G means a maximal torsion-free subgroup of G. (NK/ΩEK)* is shortly denoted by and (G1 : G2) is, as usual, the index of a subgroup G2 in G1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 73 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

1) H. Hasse defined the “Einheitenindex” QK for imaginary number fields in his book “Über die Klassenzahl abelscher Zahlkörper” and for some real number fields in, his work “Arithmetische bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörper”, Abh. Deutsch. Akad. d. Wiss. zu Berlin, Math.-Naturw. Kl., Jahrg. 1948, Nr. 2 (1950). For the real absolute abelian extension, H. W. Leopoldt defined it in his work “Über Einheitengruppe und Klassenzahl reeller abelscher Zahlkörper”, Abh. Deutsch. Akad. d. Wiss. zu Berlin, Math.-Naturw. Kl., Jahrg. 1953, Nr. 2 (1954).

2) Cf. the latter work by H. Hasse in 1).

3) Cf. S. Kuroda, “Über den Dirichletschen Körper”, J. Fac. Sci. Imp. Univ. Tokyo, Sec. I, Vol. IV, Part 5 (1943).

T. Kubota, “Über den bizyklischen biquadratischen Zahlkörper”, Nagoya Math. J., 10 (1956).