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arXiv · 1709.08453

Some examples of quadratic fields with finite nonsolvable maximal unramified extensions II

Kwang-Seob Kim·Joachim König
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Abstract

Let $K$ be a number field and $K_{ur}$ be the maximal extension of $K$ that is unramified at all places. In a previous article, the first author found three real quadratic fields $K$ such that $Gal(K_{ur}/K)$ is finite and nonabelian simple under the assumption of the GRH(Generalized Riemann Hypothesis). In this article, we will identify more quadratic number fields $K$ such that $Gal(K_{ur}/K)$ is a finite nonsolvable group and also explicitly calculate their Galois groups under the assumption of the Generalized Riemann Hypothesis.

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Kwang-Seob Kim, Joachim König. 2017-09-25. Some examples of quadratic fields with finite nonsolvable maximal unramified extensions II. https://arxiv.org/abs/1709.08453

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