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Soit un nombre premier impair. Soit une -extension galoisienne de corps ne contenant pas les racines -ièmes de l’unité : . Notons le groupe de Galois de et son sous-groupe de Frattini. Via une notion de descente galoisienne et les parallélogrammes galoisiens qu’elle induit, nous construisons ici toutes les extensions telles que soit d’ordre .
Tout entier algébrique irrationnel a deux conjugués éloignés d’au moins .
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