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Class groups of dihedral extensions. (English) Zbl 1067.11069

The first part of the paper is a readable overview of reflection theorems for algebraic number fields. The second part considers dihedral extensions \(L/F\) of algebraic number fields of degree \(2p\) for an odd prime \(p\). The author proves relations between the \(p\)-ranks of the class groups of the quadratic and the non-normal subextension of \(L/F\). He generalizes and extends previous results by R. Bölling [Math. Nachr. 135, 275–310 (1988; Zbl 0674.12003)].

MSC:

11R29 Class numbers, class groups, discriminants
11R16 Cubic and quartic extensions

Citations:

Zbl 0674.12003
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References:

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