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arXiv · 2010.14790

On unramified solvable extensions of small number fields

Joachim König
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Abstract

We investigate unramified extensions of number fields with prescribed solvable Galois group and certain extra conditions. In particular, we are interested in the minimal degree of a number field $K$, Galois over $\mathbb{Q}$, such that $K$ possesses an unramified $G$-extension. We improve the best known bounds for the degree of such number fields $K$ for certain classes of solvable groups, in particular nilpotent groups.

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Joachim König. 2020-10-28. On unramified solvable extensions of small number fields. https://doi.org/10.1017/s0004972720001136

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