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Norms in finite Galois extensions of the rationals. (English) Zbl 0686.12006

It is shown that, except for a certain special case, a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.
Reviewer: H.Opolka

MSC:

11R37 Class field theory
11R04 Algebraic numbers; rings of algebraic integers
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