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Ranks of Sylow 3-subgroups of ideal class groups of certain cubic fields. (English) Zbl 0268.12001


MSC:

11R18 Cyclotomic extensions
11R16 Cubic and quartic extensions
11R37 Class field theory
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References:

[1] Pierre Barrucand and Harvey Cohn, A rational genus, class number divisibility, and unit theory for pure cubic fields, J. Number Theory 2 (1970), 7 – 21. · Zbl 0192.40001 · doi:10.1016/0022-314X(70)90003-X
[2] Pierre Barrucand and Harvey Cohn, Remarks on principal factors in a relative cubic field, J. Number Theory 3 (1971), 226 – 239. · Zbl 0218.12002 · doi:10.1016/0022-314X(71)90040-0
[3] Helmut Hasse, Zur arithmetischen Theorie der algebraischen Funktionenkörper, Jber. Deutsch. Math. Verein 52 (1942), 1 – 48 (German). · JFM 68.0057.01
[4] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Ia, Jber. Deutsch. Math. -Verein. 36 (1927), 233-311. · JFM 53.0143.01
[5] A. Borel, S. Chowla, C. S. Herz, K. Iwasawa, and J.-P. Serre, Seminar on complex multiplication, Seminar held at the Institute for Advanced Study, Princeton, N.J., 1957-58. Lecture Notes in Mathematics, No. 21, Springer-Verlag, Berlin-New York, 1966. · Zbl 0147.03902
[6] Heinrich-Wolfgang Leopoldt, Zur Struktur der \?-Klassengruppe galoisscher Zahlkörper, J. Reine Angew. Math. 199 (1958), 165 – 174 (German). · Zbl 0082.25402 · doi:10.1515/crll.1958.199.165
[7] Hideo Wada, On cubic Galois extensions of \?(\sqrt -3), Proc. Japan Acad. 46 (1970), 397 – 400. · Zbl 0209.35605
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