Primitive finitary skew linear groups
type: Item
instance of: scholarly article
title: Primitive finitary skew linear groups
zbMATH Open document ID: 0798.20041
DOI: 10.1007/BF01196427
published in: Archiv der Mathematik
publication date: 1994-11-09T00:00:00Z
review text: We discuss normal subgroups \(N\) of primitive subgroups \(G\) of the finitary general linear group \(FLG(V)\) of any vector space \(V\) over any division ring \(D\). Usually we assume some solubility restriction on \(N\). As a corollary of our main result we have the following. Let \(G\) be a primitive irreducible subgroup of \(FGL(V)\). If either, \(G\) is hyper locally nilpotent (that is radical in the sense of Kurosh), or, \(G\) is locally soluble and \(D\) is locally finite-dimensional over its centre, then \(V\) has finite dimension over \(D\).
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 590066
zbMATH Keywords: normal subgroups
zbMATH Keywords: primitive subgroups
zbMATH Keywords: finitary general linear group
zbMATH Keywords: division ring
zbMATH Keywords: primitive irreducible subgroup
zbMATH Keywords: hyper locally nilpotent
zbMATH Keywords: locally soluble
zbMATH Keywords: finite dimension
author: B. A. F. Wehrfritz
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
cites work: The lawlessness of groups of finitary permutations
cites work: Q3737662
cites work: Crossed product criteria and skew linear groups
cites work: Locally soluble finitary skew linear groups
cites work: Locally Nilpotent Finitary Skew Linear Groups
cites work: Algebras generated by locally nilpotent finitary skew linear groups
cites work: Irreducible locally nilpotent finitary skew linear groups
full work available at URL: https://doi.org/10.1007/bf01196427
OpenAlex ID: W1969411924
description: scientific article; zbMATH DE number 590066