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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Genera in abelian extensions


Author: Robert Gold
Journal: Proc. Amer. Math. Soc. 47 (1975), 25-28
DOI: https://doi.org/10.1090/S0002-9939-1975-0354613-1
MathSciNet review: 0354613
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Abstract | References | Additional Information

Abstract: The principal genus in an abelian extension is characterized as the kernel of norm residue symbols at the ramified primes.


References [Enhancements On Off] (What's this?)

  • [1] Y. Furuta, Über die zentrale Klassenzahl eines Relativgaloisschen Zahlkörpers, J. Number Theory 3 (1971), 318-322. MR 45 #6795. MR 0297743 (45:6795)
  • [2] C. F. Gauss, Untersuchungen über höhere Arithmetik, Chelsea, New York, 1965. MR 32 #5488.
  • [3] F. Halter-Koch, Ein Satz über die Geschlechter relativ-zyklischer Zahlkörper von Primzahlgrad und seine Anwendung auf biquadratisch-bizyklische Körper, J. Number Theory 4 (1972), 144-156. MR 46 #1756. MR 0302612 (46:1756)
  • [4] H. Hasse, A supplement to Leopoldt's theory of genera in abelian number fields, J. Number Theory 1 (1969), 4-7. MR 39 #2733. MR 0241393 (39:2733)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0354613-1
Keywords: Genera, norm residue, genus field
Article copyright: © Copyright 1975 American Mathematical Society

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