Genus group of finite Galois extensions
Author:
Teruo Takeuchi
Journal:
Proc. Amer. Math. Soc. 98 (1986), 211-214
MSC:
Primary 11R37
DOI:
https://doi.org/10.1090/S0002-9939-1986-0854020-6
MathSciNet review:
854020
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Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be a Galois extension of finite degree, and let 
denote the maximal abelian extension over 
contained in the Hilbert class field of 
. We give formulas about the group structure of 
and the genus group of 
, which refine the ordinary genus formula.
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- [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
- [4] I. R. Šfarevič, Extensions with given points of ramification, Inst. Hautes Études Sci. Publ. Math. 18 (1963), 71-95; Amer. Math. Soc. Transl. 59 (1966), 128-149.
-extension of a finite algebraic number field with given ramification, Nagoya Math. J. 70 (1978), 183-202. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R37
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1986-0854020-6
Article copyright:
© Copyright 1986
American Mathematical Society