On the l-class rank in some algebraic number fields

Shinju KOBAYASHI

doi:10.2969/jmsj/02640668

Shinju KOBAYASHI

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1974 Volume 26 Issue 4 Pages 668-676

DOI https://doi.org/10.2969/jmsj/02640668

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Published: 1974 Received: May 12, 1973 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. Gras, Sur les l-classes d'idéaux Bans les extensions cycliques relatives de degré premier l, to appear in Ann. Inst. Fourier.
2) H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Ia, Jber. Deutsch. Math.-Verein., 36 (1927), 231-311.
3) T. Honda, Pure cubic fields whose class numbers are multiples of 3, J. Number Theory, 3 (1971), 7-12.
4) S. Kobayashi, On the l-dimension of the ideal class groups of Kummer extensions of a certain type, J. Fac. Sci. Univ. Tokyo Sec. IA, 18 (1971), 399-404.
5) S. Kobayashi, On the 3-rank of the ideal class groups of certain pure cubic fields, to appear J. Fac. Sci. Univ. Tokyo Sec.
6) J. Martinet, Sur l'arithmétique des extensions galoisiennes à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier, 19 (1969), 1-80.
7) J. Porusch, Die Arithmetik in Zahlkörpern, deren zugehörige Galoissche Körper spezielle metabelsche Gruppen bezitzen, auf klassenkörpertheoretischer Grundlage, Math. Z., 37 (1933), 134-160.
8) P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc., 44 (1969), 31-38.

Right : [1] G. Gras, Sur les l-classes d'idéaux Bans les extensions cycliques relatives de degré premier l, to appear in Ann. Inst. Fourier.
[2] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Ia, Jber. Deutsch. Math.-Verein., 36 (1927), 231-311.
[3] T. Honda, Pure cubic fields whose class numbers are multiples of 3, J. Number Theory, 3 (1971), 7-12.
[4] S. Kobayashi, On the l-dimension of the ideal class groups of Kummer extensions of a certain type, J. Fac. Sci. Univ. Tokyo Sec. IA, 18 (1971), 399-404.
[5] S. Kobayashi, On the 3-rank of the ideal class groups of certain pure cubic fields, to appear J. Fac. Sci. Univ. Tokyo Sec. IA, 18 (1971), 399-404.
[6] J. Martinet, Sur l'arithmétique des extensions galoisiennes à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier, 19 (1969), 1-80.
[7] J. Porusch, Die Arithmetik in Zahlkörpern, deren zugehörige Galoissche Körper spezielle metabelsche Gruppen bezitzen, auf klassenkörpertheoretischer Grundlage, Math. Z., 37 (1933), 134-160.
[8] P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc., 44 (1969), 31-38.

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