Unramified extensions of quadratic number fields with Galois group $2.A_n$

Joachim König

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arXiv · 2505.10100

Unramified extensions of quadratic number fields with Galois group $2.A_n$

Joachim König

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Abstract

We realize infinitely many covering groups $2.A_n$ (where $A_n$ is the alternating group) as the Galois group of everywhere unramified Galois extensions over infinitely many quadratic number fields. After several predecessor works investigating special cases or proving conditional results in this direction, these are the first unramified realizations of infinitely many of these groups.

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Joachim König. 2025-05-15. Unramified extensions of quadratic number fields with Galois group $2.A_n$. https://arxiv.org/abs/2505.10100

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