Displaying similar documents to “Extensions having reduced subextensions.”

A classification of the extensions of degree p 2 over p whose normal closure is a p -extension

Luca Caputo (2007)

Journal de Théorie des Nombres de Bordeaux

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Let k be a finite extension of p and k be the set of the extensions of degree p 2 over k whose normal closure is a p -extension. For a fixed discriminant, we show how many extensions there are in p 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 k .

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

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The Steinitz class of a number field extension K / k is an ideal class in the ring of integers 𝒪 k of k , which, together with the degree [ K : k ] of the extension determines the 𝒪 k -module structure of 𝒪 K . We denote by R t ( k , G ) the set of classes which are Steinitz classes of a tamely ramified G -extension of k . We will say that those classes are realizable for the group G ; it is conjectured that the set of realizable classes is always a group. In this paper we will develop some of the ideas contained...

PAC fields over number fields

Moshe Jarden (2006)

Journal de Théorie des Nombres de Bordeaux

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We prove that if K is a number field and N is a Galois extension of which is not algebraically closed, then N is not PAC over K .