On a theorem of Koch
type: Item
instance of: scholarly article
title: On a theorem of Koch
zbMATH Open document ID: 0879.11066
author: Farshid Hajir
published in: Pacific Journal of Mathematics
publication date: 1998-01-18T00:00:00Z
review text: The author studies the question of which quadratic number fields have infinite 2-class field tower. He strengthens a theorem of the reviewer [cf. \textit{H. Koch}, J. Reine Angew. Math. 214/215, 201-206 (1964; Zbl 0123.03904)] about such fields with class group containing a subgroup of type (4, 4, 4). His method of proof is different from the method of the reviewer. He uses a theorem of \textit{J. Martinet} [Invent. Math. 44, 65-73 (1978; Zbl 0369.12007)] about infinite 2-class towers for fields of higher degree. Furthermore, the author gives some new interesting examples of infinite class field towers.
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 1025799
zbMATH Keywords: quadratic number fields
zbMATH Keywords: infinite class field towers
reviewed by: Helmut Koch
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.15
OpenAlex ID: W1586013205
DOI: 10.2140/PJM.1996.176.15
description: scientific article; zbMATH DE number 1025799