The Exponent 2-Class-Group Problem for Non-Galois Over Q Quartic Fields That Are Quadratic Extensions of Imaginary Quadratic Fields

Abstract

Focusing on a particular case, we will show that one can explicitly determine the quartic fields K that have ideal class groups of exponent ≤ 2, provided that K/ Q is not normal, provided that K is a quadratic extension of a fixed imaginary quadratic number field, and provided that the regulator of K is not too large compared with the discriminant of K.