Soluble normal subgroups of skew linear groups
type: Item
instance of: scholarly article
title: Soluble normal subgroups of skew linear groups
zbMATH Open document ID: 0604.20051
DOI: 10.1016/0022-4049(86)90063-0
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let P(U\(\cup LF)\) be the class of all groups with a normal series of finite length whose factors are abelian or locally finite. Let D be a division ring, \(D^{n\times n}\) the matrix ring of degree n over D and GL(n,D) the group of units of \(D^{n\times n}\). Let F be a centre of D. A group \(G\subset GL(n,D)\) is called absolutely irreducible if the F- enveloping algebra of G in \(D^{n\times n}\) coincides with \(D^{n\times n}.\) The main result of this article is the following theorem: Let \(G\subset GL(n,D)\) be an absolutely irreducible group and H a normal P(U\(\cup LF)\)- subgroup of G. (i) H contains an abelian normal subgroup A of G with H/A locally finite and \(G/C_ G(H)\) is abelian by periodic; (ii) if H modulo its centre is periodic then \(G/C_ G(H)\) is periodic.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 20E25
zbMATH DE Number: 3975224
zbMATH Keywords: normal series of finite length
zbMATH Keywords: division ring
zbMATH Keywords: matrix ring
zbMATH Keywords: group of units
zbMATH Keywords: centre
zbMATH Keywords: absolutely irreducible group
zbMATH Keywords: abelian normal subgroup
zbMATH Keywords: locally finite
author: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90063-0
OpenAlex ID: W2008621141
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description: scientific article; zbMATH DE number 3975224