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We determine all cyclic extensions of prime degree over a -regular number field containing the -roots of unity which are also -regular. We classify these extensions according to the ramification index of the wild place in and to the -valuation of the relative class number (which is the quotient of the ordinary class numbers of and ).
We study the case where the is odd prime, since the even case was studien by R. Berger. Our genus theory methods rely essentially on G. Gras...
Dans cet article, nous déterminons et classifions toutes les extensions cycliques de degré de corps de nombres -rationnels contenant une racine primitive -ième de l’unité. (Cette notion est plus générale que celle de -régularité étudiée dans un travail antérieur).
We present an algorithm for computing the 2-group of the positive divisor classes in case the number field has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel in .
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