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On the maximal unramified pro-2-extension of Z2-extensions of certain real quadratic fields

โœ Scribed by Yasushi Mizusawa

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
230 KB
Volume
105
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

In this paper, we construct an infinite family of real quadratic fields k such that the maximal unramified pro-2-extension of the cyclotomic Z 2 -extension of k is a finite non-abelian extension.

๐Ÿ“œ SIMILAR VOLUMES

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Let K=Q(-m) be a real quadratic number field. In this article, we find a necessary and sufficient condition for K to admit an unramified quadratic extension with a normal integral basis distinct from K(-&1), provided that the prime 2 splits neither in Kร‚Q nor in Q(-&m)ร‚Q, in terms of a congruence sa

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Assume that \(K\) is either a totally real or a totally imaginary number field. Let \(F\) be the maximal unramified elementary abelian 2-extension of \(K\) and \([F: K]=2^{n}\). The purpose of this paper is to describe a family of cubic cyclic extension of \(K\). We have constructed an unramified ab