Genus group of finite Galois extensions
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- by Teruo Takeuchi PDF
- Proc. Amer. Math. Soc. 98 (1986), 211-214 Request permission
Abstract:
Let $K/k$ be a Galois extension of finite degree, and let $Kā€™$ denote the maximal abelian extension over $k$ contained in the Hilbert class field of $K$. We give formulas about the group structure of $Gal(Kā€™/k)$ and the genus group of $K/k$, which refine the ordinary genus formula.References
- Yoshiomi Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J. 29 (1967), 281ā€“285. MR 209260
- Tomio Kubota, Galois group of the maximal abelian extension over an algebraic number field, Nagoya Math. J. 12 (1957), 177ā€“189. MR 98077
- Hiroo Miki, On the maximal Abelian $l$-extension of a finite algebraic number field with given ramification, Nagoya Math. J. 70 (1978), 183ā€“202. MR 480420 I. R. Å fareviĨ, Extensions with given points of ramification, Inst. Hautes Ɖtudes Sci. Publ. Math. 18 (1963), 71-95; Amer. Math. Soc. Transl. 59 (1966), 128-149.
Additional Information
- © Copyright 1986 American Mathematical Society
- 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