Unramified extensions of quadratic number fields with certain perfect Galois groups

Abstract

In this paper, we provide infinite families of quadratic number fields with everywhere unramified Galois extensions of Galois group [Formula: see text] and [Formula: see text], respectively. To my knowledge, these are the first instances of infinitely many such realizations for perfect groups which are not generated by involutions, a property which makes them difficult to approach for the problem in question and leads to somewhat delicate local–global problems in inverse Galois theory.