On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.
Chipchakov, Ivan D. (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Chipchakov, Ivan D. (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Luca Caputo (2007)
Journal de Théorie des Nombres de Bordeaux
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Let be a finite extension of and be the set of the extensions of degree over whose normal closure is a -extension. For a fixed discriminant, we show how many extensions there are in with such discriminant, and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalized to get a classification of the extensions in .
James Carter (1998)
Colloquium Mathematicae
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Alessandro Cobbe (2010)
Journal de Théorie des Nombres de Bordeaux
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The Steinitz class of a number field extension is an ideal class in the ring of integers of , which, together with the degree of the extension determines the -module structure of . We denote by the set of classes which are Steinitz classes of a tamely ramified -extension of . We will say that those classes are realizable for the group ; it is conjectured that the set of realizable classes is always a group. In this paper we will develop some of the ideas contained...
Khrebtova, Ekaterina, Malinin, Dmitry (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Moshe Jarden (2006)
Journal de Théorie des Nombres de Bordeaux
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We prove that if is a number field and is a Galois extension of which is not algebraically closed, then is not PAC over .
James Carter (1996)
Colloquium Mathematicae
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