On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields

Abstract

Inspired by the Odlyzko root discriminant and Golod-Shafarevich p-group bounds, Martinet (1978) asked whether an imaginary quadratic number field K/Q must always have an infinite Hilbert 2-class field tower when the class group of K has 2-rank 4, or equivalently when the discriminant of K has 5 prime factors. No negative results are known. Benjamin (