Maximal abelian normal subgroups of Galois pro-2-groups
type: Item
instance of: scholarly article
title: Maximal abelian normal subgroups of Galois pro-2-groups
zbMATH Open document ID: 0809.12004
author: Antonio Engler
author: João Bosco Nogueira
published in: Journal of Algebra
publication date: 1994-08-17T00:00:00Z
review text: Let \(K\) be a field, \(\text{char} \neq 2\). Abelian normal subgroups of the pro-2-group \(\text{Gal} (K(2)/K)\), where \(K(2)\) is the quadratic closure of \(K\), were objects of interest of many papers. Under various additional assumptions on the field \(K\), \textit{R. Ware} [Pac. J. Math. 76, 541-564 (1978; Zbl 0405.12019), Commun. Algebra 13, 1713-1736 (1985; Zbl 0569.10008), Rocky Mt. J. Math. 19, 985-995 (1989; Zbl 0706.11023)] managed to point out a relatively large abelian normal subgroup of \(\text{Gal} (K(2)/K)\) with fully described structure (or at least rank). In this paper the authors show that the group \(\text{Gal} (K(2)/K)\) always contains the largest abelian normal subgroup. The details on the structure of this subgroup are in a strict relation to Ware's results.
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 11E04
zbMATH DE Number: 614242
zbMATH Keywords: quadratic closure
zbMATH Keywords: 2-henselian valuation ring
MaRDI profile type: Publication
full work available at URL: jabr.1994.1164
OpenAlex ID: W2046828300
DOI: 10.1006/JABR.1994.1164
description: scientific article; zbMATH DE number 614242