On the normal structure of the general linear group over a ring
type: Item
instance of: scholarly article
title: On the normal structure of the general linear group over a ring
zbMATH Open document ID: 0930.20045
DOI: 10.1007/BF02169976
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-10-05T00:00:00Z
review text: The author discusses the normal structure of general linear groups over rings [compare \textit{H. Bass}, Algebraic K-theory, New York-Amsterdam: W. A. Benjamin (1968; Zbl 0174.30302)], and centrality of \(K_2(n,R)\) in the Steinberg group \(\text{St}(n,R)\). For instance, he shows that if \(n\geq\text{sr}(R,I)+2\), then the centrality of \(K_2(n,R)\) in \(\text{St}(n,R)\) is equivalent to the centrality of \(K_2(n,R/I)\) in \(\text{St}(n,R/I)\). Similarly he compares the standardness of the normal structure of \(\text{GL}(n,R)\) with the standardness of the normal structure of \(\text{GL}(n,R/I)\).
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 19C20
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 18F30
Mathematics Subject Classification ID: 19B10
zbMATH DE Number: 1337579
zbMATH Keywords: general linear groups over rings
zbMATH Keywords: normal subgroups
zbMATH Keywords: centrality
zbMATH Keywords: Steinberg groups
zbMATH Keywords: \(K_2\)
author: Alexei Stepanov
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1337579