Unramified extensions of quadratic number fields with Galois group SL₂(7)

2021/09/20 by Joachim König, König, Joachim · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.09646

openalex publication_date 2021/09/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/02

Abstract

We provide an infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group SL₂(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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• Unramified extensions of quadratic number fields with Galois group 2.A_n

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