Class field towers of imaginary quadratic fields
type: Item
instance of: scholarly article
title: Class field towers of imaginary quadratic fields
zbMATH Open document ID: 0611.12009
DOI: 10.1007/BF01168670
author: James R. Brink
author: Robert Gold
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155204
review text: Let \(F\) be an imaginary quadratic field whose ideal class group has an elementary abelian Sylow 3-subgroup of order \(3^ 2\). \textit{A. Scholz} and \textit{O. Taussky} [J. Reine Angew. Math. 171, 19--41 (1934; Zbl 0009.10202)] proved that if \(F\) has a certain capitulation type then the 3-class field tower of \(F\) is of length 2. The present authors prove this in a simpler way. For another particular capitulation type they show, by constructing a group theoretic example, that it is possible for the 3-class field tower to be of length 3. This corrects an assertion made by Scholz and Taussky [op. cit.].
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 3987398
zbMATH Keywords: imaginary quadratic field
zbMATH Keywords: ideal class group
zbMATH Keywords: class field tower
zbMATH Keywords: capitulation
MaRDI profile type: Publication
cites work: On a special class of \(p\)-groups
cites work: Q3253828
cites work: Q4756548
description: scientific article; zbMATH DE number 3987398