Normal subgroups of classical groups over rings
type: Item
instance of: scholarly article
title: Normal subgroups of classical groups over rings
zbMATH Open document ID: 0843.20037
DOI: 10.1016/0022-4049(94)00144-8
author: Hong You
author: L. N. Vaserstein
published in: Journal of Pure and Applied Algebra
publication date: 1996-08-15T00:00:00Z
review text: The normal subgroup problem for a classical group \(G\) over a ring \(R\) is to study whether the ``sandwich theorem'' holds, i.e., for any subgroup \(H\) of \(G\) normalized by the elementary subgroup of \(G\), there is a unique ideal \(J\) of \(R\), such that \(H\) lies between the general and elementary congruence subgroups with respect to \(J\). The authors prove that, for the pseudo-orthogonal groups over a wide class of rings, containing every ring which is finitely generated as a module over its center, the normal subgroup problem has a positive solution. It covers many previous relevant results.
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20H25
zbMATH DE Number: 856980
zbMATH Keywords: sandwich theorem
zbMATH Keywords: normal subgroup problem
zbMATH Keywords: elementary subgroups
zbMATH Keywords: congruence subgroups
zbMATH Keywords: pseudo-orthogonal groups
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)00144-8
OpenAlex ID: W2123323843
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description: scientific article; zbMATH DE number 856980