Bases normales d'entiers relatives quadratiques

Abstract

Let K be any number field, and let E be a quadratic or a biquadratic extension of K. We give necessary conditions for the existence of a field N, respectively, cyclic of degree 4, dihedral or quaternionian of degree 8, over K, which admits a normal integral basis over E. When the class number of K is h( K) = 1, we prove that these conditions are also sufficient, and we provide explicit formulae to construct normal integral bases of N over E.