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Quartic fields with large class numbers. (English) Zbl 1448.11201

In this paper, the authors show that there exist infinitely many quartic number fields \(K\) with large class numbers such that \(K/\mathbb Q\) is a Galois extension whose Galois group is isomorphic to a given finite group. P. J. Cho and H. H. Kim [J. Théor. Nombres Bordx. 24, No. 3, 583–603 (2012; Zbl 1275.11145)] proved that there are infinitely many totally real cyclic extensions over \(\mathbb Q\) of degree 4 with large class numbers. In this paper, the authors consider all the other cases of quartic Galois extensions (totally real biquadratic extensions, biquadratic CM-fields and quartic cyclic CM-fields).

MSC:

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

Citations:

Zbl 1275.11145
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References:

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