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arXiv · 2109.09646

Unramified extensions of quadratic number fields with Galois group $SL_2(7)$

Joachim König
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Abstract

We provide an infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group $SL_2(7)$. To my knowledge, this is the first instance of infinitely many such realizations for a perfect group which is not generated by involutions, a property which makes it difficult to approach for the problem in question and leads to somewhat delicate local-global problems in inverse Galois theory.

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Joachim König. 2021-09-20. Unramified extensions of quadratic number fields with Galois group $SL_2(7)$. https://arxiv.org/abs/2109.09646

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