Hilbert-Speiser number fields and the complex conjugation

Abstract

Let p be a prime number. We say that a number field F satisfies the condition (H_p) when any tame cyclic extension N⁄F of degree p has a normal integral basis. We determine all the CM Galois extensions F⁄Q satisfying (H_p) for the case p≥5, using the action of the complex conjugation on several objects associated to F.