Quadratic number fields with unramified SL2(5)-extensions

Abstract

Continuing the line of thought of an earlier work [11], we provide the first infinite family of quadratic number fields with everywhere unramified Galois extensions of Galois group SL2(5), the (unique) smallest nonsolvable group for which this problem was previously open. Our approach also improves upon [11] 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.