# zbMATH — the first resource for mathematics

Décomposition des nombres premièrs dans des extensions non abéliennes. (French) Zbl 0326.12005
Summary: Let $$K$$ be a number field normal over $$\mathbb Q$$ with Galois group $$G$$ containing a normal abelian subgroup $$H$$ with the following properties: $$H$$ is of odd order if its fixed field is a real field of degree greater than 2 and the “Verlagerung” application associated with $$H$$ is trivial. It is shown that the decomposition of a prime number in $$K$$ depends on its representation by some forms with integral coefficients and with degree and number of variables equal to the index of $$H$$ in $$G$$.

##### MSC:
 11R21 Other number fields 11E76 Forms of degree higher than two
##### Keywords:
decomposition of prime numbers; nonabelian extensions
Full Text:
##### References:
 [1] GAUSS, Arithmetishe untersuchungen, Werke Bd (traduction française : Blanchard ; traduction anglaise : Yale Univ. Press). [2] BOREVICH, SHAFAREVICH, Théorie des nombres, Monographie internationale de Math. Moderne n° 8, Gauthier-Villard. · Zbl 0145.04901 [3] ARTIN, TATE, Class field theory, Harvard (1961). [4] EMMA LEHMER, Cubic and quintic residue, Duke Math. Journal, 18 (1951).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.