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Currently displaying 1 – 2 of 2

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Steinitz classes of tamely ramified nonabelian extensions of odd prime power order

Alessandro Cobbe — 2011

Acta Arithmetica

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe — 2010

Journal de Théorie des Nombres de Bordeaux

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 in [...

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