Residual properties of finitary linear groups
type: Item
instance of: scholarly article
title: Residual properties of finitary linear groups
zbMATH Open document ID: 0807.20038
author: Brunella Bruno
author: Richard E. Phillips
published in: Journal of Algebra
publication date: 1994-08-17T00:00:00Z
review text: A finitary linear group is a group \(G\) of automorphisms of a vector space of infinite dimension over a field such that every element \(g \in G\) fixes elementwise a subspace of finite codimension. Let \(G\) be a finitary group. The main result of the paper under review asserts that every \(G\)-composition factor is of finite dimension provided one of the following holds: (a) \(G\) is both residually solvable and locally solvable; (b) \(G\) is residually finite, locally finite and no element of \(G\) is of order equal to the characteristic of the ground field.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 614234
zbMATH Keywords: finite dimensional composition factors
zbMATH Keywords: finitary linear group
zbMATH Keywords: residually solvable groups
zbMATH Keywords: locally solvable groups
zbMATH Keywords: residually finite groups
zbMATH Keywords: locally finite groups
MaRDI profile type: Publication
full work available at URL: jabr.1994.1158
OpenAlex ID: W2053436848
DOI: 10.1006/JABR.1994.1158
description: scientific article; zbMATH DE number 614234