An example of a $\mathop {\rm PSL}\nolimits _2(\mathbb {F}_7)$-maximal unramified extension of a quartic number field
Volume 179 / 2017
Acta Arithmetica 179 (2017), 147-162
MSC: Primary 11R37; Secondary 11F80, 11R29.
DOI: 10.4064/aa8506-2-2017
Published online: 7 July 2017
Abstract
Let $K$ be a number field and $K^{f}_{\rm ur}$ be the maximal extension of $K$ which is unramified over all finite places. We find a quartic field $K$ such that $\operatorname{Gal}(K^f_{\rm ur}/K) \simeq \operatorname{PSL}_2(\mathbb F_7)$ under the assumption of the GRH.
