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On dit qu’un corps est de Hilbert-Speiser en un premier si toute extension modérée abélienne finie de degré admet une base normale entière. On dit qu’un corps est de Hilbert-Speiser s’il est de Hilbert-Speiser pour tout premier . Il est bien connu que est un tel corps. Dans un article [3] de 1998, Greither, Replogle, Rubin et Srivastav ont montré que était le seul corps de Hilbert-Speiser. On donne ici une condition nécessaire et suffisante pour qu’un corps soit de Hilbert-Speiser en ....
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