Finitary linear transformation groups and elements of finite local degree
type: Item
instance of: scholarly article
title: Finitary linear transformation groups and elements of finite local degree
zbMATH Open document ID: 0619.20022
DOI: 10.1007/BF01190224
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: A linear transformation g of the vector space V is said to be finitary if V(g-1) is finite dimensional. The elements of GL(V) which are finitary form a normal subgroup FGL(V) (equal to GL(V) when V is finite dimensional). A representation is finitary if all elements are represented by finitary linear transformations. This paper provides a local characterization of those elements g of the group G for which there is a faithful representation of G with the image of g finitary. A consequence is that the simple group G has a faithful finitary representation if and only if each of its countable simple subgroups has a faithful finitary representation.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4004464
zbMATH Keywords: finitary linear transformations
zbMATH Keywords: local characterization
zbMATH Keywords: simple group
zbMATH Keywords: faithful finitary representation
zbMATH Keywords: countable simple subgroups
author: J. I. Hall
MaRDI profile type: Publication
cites work: Infinite alternating groups as finitary linear transformation groups
cites work: Q5675882
full work available at URL: https://doi.org/10.1007/bf01190224
OpenAlex ID: W2043866573
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description: scientific article; zbMATH DE number 4004464