Quadratic number fields with unramified $SL_2(5)$-extensions
Number Theory
2022-11-04 v1
Abstract
Continuing the line of thought of an earlier work, we provide the first infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group , the (unique) smallest nonsolvable group for which this problem was previously open. Our approach also improves upon previous work by yielding the first infinite family of real-quadratic fields possessing an unramified Galois extension whose Galois group is perfect and not generated by involutions. Our result also amounts to a new existence result on quintic number fields with squarefree discriminant and additional local conditions.
Cite
@article{arxiv.2211.01555,
title = {Quadratic number fields with unramified $SL_2(5)$-extensions},
author = {Joachim König},
journal= {arXiv preprint arXiv:2211.01555},
year = {2022}
}