Literatur
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.
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.
Cf. H. Zassenhaus, Lehrbuch der Gruppentheorie I (Leipzig und Berlin 1937), p. 104.
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Iwasawa, K. A note on class numbers of algebraic number fields. Abh. Math. Semin. Univ. Hambg. 20, 257–258 (1956). https://doi.org/10.1007/BF03374563
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DOI: https://doi.org/10.1007/BF03374563