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A note on class numbers of algebraic number fields. (English) Zbl 0074.03002

MSC:
11R29 Class numbers, class groups, discriminants
11R20 Other abelian and metabelian extensions
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[1] Cf. H. Hasse, Über die Klassenzahl Abelscher Zahlkörper (Berlin, 1952), § 34. The author expresses here his hearty thanks to Professor H. Hasse for his kind suggestions in preparing the present paper.
[2] This first part is a known result; cf. C. CHEVALLEY, Relation entre le nombre de classes d’un sous-corps et celui d’un sur-corps. C. R., Paris, 192, 257–258 (1931). The proof is given here only for the sake of completeness.
[3] Cf. H. Zassenhaus, Lehrbuch der Gruppentheorie I (Leipzig und Berlin 1937), p. 104.
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