## 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

### Keywords:

class numbers; quartic fields

Zbl 1275.11145
Full Text:

### References:

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