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Proceedings of the American Mathematical Society
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
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] Yoshiomi Furuta, Über die Zentrale Klassenzahl eines relativ-galoisschen Zahlkörpers, J. Number Theory 3 (1971), 318–322 (German, with English summary). MR 0297743 (45 #6795)
  • [2] C. F. Gauss, Untersuchungen über höhere Arithmetik, Chelsea, New York, 1965. MR 32 #5488.
  • [3] Franz 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 (German, with English summary). MR 0302612 (46 #1756)
  • [4] Helmut Hasse, A supplement to Leopoldt’s theory of genera in abelian number fields., J. Number Theory 1 (1969), 4–7. MR 0241393 (39 #2733)

Additional Information

PII: S 0002-9939(1975)0354613-1
Keywords: Genera, norm residue, genus field
Article copyright: © Copyright 1975 American Mathematical Society

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