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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Genus group of finite Galois extensions

Author: Teruo Takeuchi
Journal: Proc. Amer. Math. Soc. 98 (1986), 211-214
MSC: Primary 11R37
MathSciNet review: 854020
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Abstract: Let $ K/k$ be a Galois extension of finite degree, and let $ K'$ denote the maximal abelian extension over $ k$ contained in the Hilbert class field of $ K$. We give formulas about the group structure of $ Gal(K'/k)$ and the genus group of $ K/k$, which refine the ordinary genus formula.

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

  • [1] Yoshiomi Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J. 29 (1967), 281–285. MR 0209260 (35 #162)
  • [2] Tomio Kubota, Galois group of the maximal abelian extension over an algebraic number field, Nagoya Math. J. 12 (1957), 177–189. MR 0098077 (20 #4539)
  • [3] Hiroo Miki, On the maximal Abelian 𝑙-extension of a finite algebraic number field with given ramification, Nagoya Math. J. 70 (1978), 183–202. MR 0480420 (58 #583)
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PII: S 0002-9939(1986)0854020-6
Article copyright: © Copyright 1986 American Mathematical Society

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