Nilpotence in finitary linear groups
type: Item
instance of: scholarly article
title: Nilpotence in finitary linear groups
zbMATH Open document ID: 0807.20040
published in: Michigan Mathematical Journal
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. The paper under review studies radicals of \(G\) related to the locally nilpotent one. The author considers 13 types of radicals and analyzes which of them coincide in the class of finitary linear groups. A typical result shows that the locally nilpotent radical coincides with the Gruenberg radical constituted by the set of elements \(g \in G\) such that \(\langle g\rangle\) is a member of a finite ascending series of subnormal subgroups.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 614379
zbMATH Keywords: finitary linear groups
zbMATH Keywords: radicals
zbMATH Keywords: locally nilpotent radical
zbMATH Keywords: Gruenberg radical
zbMATH Keywords: ascending series
zbMATH Keywords: subnormal subgroups
author: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004828
OpenAlex ID: W1965085629
DOI: 10.1307/MMJ/1029004828
description: scientific article; zbMATH DE number 614379