Extensions with Galois group Hol(C8) unramified over a complex quadratic number field

2025/03/29 by Benjamin, Elliot, Lemmermeyer, Franz, Snyder, Chip · 1 citation
#11R20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.23027

Abstract

We study normal extensions with Galois group Hol(C₈) that are unramified over a complex quadratic subfield. The Galois group is either the semi-dihedral group or the modular group of order 16. We present an explicit construction of such fields.

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• Étale algebras and the Kummer theory of finite Galois modules

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