A note on the normality of unramified, abelian extensions of quadratic extensions

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Abstract

Let F, K and L be algebraic number fields such that {Mathematical expression}, [K:F]=2 and [L:K]=n. It is a simple consequence of the class field theory that, if L is an abelian, unramified extension of K and (n,h)=1, where h is the class number of F, then L is normal over F. The purpose of this note is to point out the necessity of the condition (n,h)=1 by constructing for any field F with even class number a tower of fields {Mathematical expression} with [K:F]=2, [L:K]=2 where L is unramified over K, but L is not normal over F.

Original languageEnglish (US)
Pages (from-to)343-349
Number of pages7
JournalManuscripta Mathematica
Volume30
Issue number4
DOIs
StatePublished - Dec 1979

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Class number
Normality
Class Field Theory
Algebraic number Field
Even number
Necessity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A note on the normality of unramified, abelian extensions of quadratic extensions. / Madden, Daniel; Velez, William Yslas.

In: Manuscripta Mathematica, Vol. 30, No. 4, 12.1979, p. 343-349.

Research output: Contribution to journalArticle

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