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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?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854020-6
PII: S 0002-9939(1986)0854020-6
Article copyright: © Copyright 1986 American Mathematical Society