A note on the normality of unramified, abelian extensions of quadratic extensions
✍ Scribed by Daniel J. Madden; William Yslas Vélez
- Publisher
- Springer
- Year
- 1979
- Tongue
- English
- Weight
- 236 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0025-2611
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📜 SIMILAR VOLUMES
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 KÂQ nor in Q(-&m)ÂQ, in terms of a congruence sa
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.
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