A note on central class fields
type: Item
instance of: scholarly article
title: A note on central class fields
zbMATH Open document ID: 0613.12008
DOI: 10.1007/BF02941604
author: Mitsuko Horie
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1987-01-01T00:00:00Z
review text: Let K be any finite Galois extension over \({\mathbb{Q}}\). The central class field \^K of K is then defined as the maximal field such that \^K is a Galois extension over \({\mathbb{Q}}\), Gal(\^K/K) is contained in the center of Gal(\^K/ \({\mathbb{Q}})\), and \^K is unramified over K in the narrow sense. Assume that Gal(K/ \({\mathbb{Q}})\cong ({\mathbb{Z}}/\ell {\mathbb{Z}})^ 2\) with \(\ell\) a prime number. In this paper, the group structure of Gal(\^K/ \({\mathbb{Q}})\) is determined. Furthermore, a certain unramified abelian \(\ell\)-extension of a cyclic field of degree \(\ell\) is considered in connection with central class fields such as the above \^K.
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 3991626
zbMATH Keywords: central extension
zbMATH Keywords: central class field
zbMATH Keywords: unramified abelian \(\ell \)- extension
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3991626