Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T23:37:07.263Z Has data issue: false hasContentIssue false
  • English
  • Français

On the central class field mod of Galois extensions of an algebraic number field

Published online by Cambridge University Press:  22 January 2016

Susumu Shirai
Susumu Shirai*
Affiliation:
Toyama Medical and Pharmaceutical University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k be the rational number field, K/k be an Abelian extension defined mod whose degree is some power of a prime l, and let be the module of K belonging to in the sense of Fröhlich [1, p. 239].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 71 , November 1978 , pp. 61 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Fröhlich, A., On fields of class two, Proc. London Math. Soc. (3), 4 (1954), 235–256.CrossRefGoogle Scholar
[2] Fröhlich, A., The genus field and genus group in finite number fields, Mathematika, 6 (1959), 40–46.CrossRefGoogle Scholar
[3] Fröhlich, A., The genus field and genus group in finite number fields, II, Mathematika, 6 (1959), 142–146.CrossRefGoogle Scholar
[4] Furuta, Y., The genus field and genus number in algebraic number fields, Nagoya Math. J., 29 (1967), 281–285.CrossRefGoogle Scholar
[5] Furuta, Y., Über die zentrale Klassenzahl eines relativ-galoisschen Zahlkörpers, Number, J. Theory, 3 (1971), 318–322.Google Scholar
[6] Furuta, Y., On nilpotent factors of congruent ideal class groups of Galois extensions, Nagoya Math. J., S2 (1976), 13–28.CrossRefGoogle Scholar
[7] Golod, E. S. and Šafarevič, I. R., On class field towers (Russian), Lzv. Akad. Nauk. SSSR, 28, 261–272. English translation in Amer. Math. Soc. Transl., (2), 48, 91–102.Google Scholar
[8] Hasse, H., Bericht fiber neuere Untersuchungen und Problème aus der Théorie der algebraischen Zahlkörper Ia, Jahr. der Deutschen Math. Ver., 36 (1927).Google Scholar
[9] Hasse, H., Normenresttheorie galoisscher Zahlkörper mit Anwendungen auf Führer und Diskriminante abelscher Zahlkörper, Journ. Fac. Sei. Tokyo Imp. Univ., 2 (1934), 477–498.Google Scholar
[10] Herbrand, J., Sur les théorèmes du genre principal et des idéaux principaux, Abh. a.d. Hamb. Math. Sem., 8 (1933), 84–92.CrossRefGoogle Scholar
[11] Iyanaga, S., Zur Théorie der Geschlechtermoduln, J. reine angew. Math., 171 (1934), 12–18.CrossRefGoogle Scholar
[12] Kuniyoshi, H. and Takahashi, S., On the principal genus theorem, Tôhoku Math. J., (2), 5 (1953), 128–131.CrossRefGoogle Scholar
[13] Masuda, K., An application of the generalized norm residue symbol, Proc. Amer. Math. Soc, 10 (1959), 245–252.CrossRefGoogle Scholar
[14] Noether, E., Der Hauptgeschlechtssatz für relativ-galoissche Zahlkörper, Math. Ann., 108 (1933), 411–419.CrossRefGoogle Scholar
[15] Roquette, P., On class field towers, Proc. instr. conf. at Brighton (Algebraic Number Theory), (1967), 231–249.Google Scholar
[16] Safarevic, I. R., Extensions with given points of ramification (Russian), Inst. Hautes Etudes Sci. Publ. Math., 18 (1963), 71–95. English translation in Amer. Math. Soc. Transl., (2), 59, 128–149.Google Scholar
[17] Serre, J. P., Local class field theory, Proc. instr. conf. at Brighton (Algebraic Number Theory), (1967), 128–161.Google Scholar
[18] Shirai, S., Central class numbers in central class field towers, Proc. Japan Acad., 51 (1975), 389–393.Google Scholar
[19] Terada, F., On the principal genus theorem concerning the abelian extensions, Tôhoku Math. J., (2), 4 (1952), 141–152.CrossRefGoogle Scholar
[20] Terada, F., A note on the principal genus theorem, Tôhoku Math. J., (2), 5 (1953), 211–213.CrossRefGoogle Scholar