Hypercentrality and hypercyclicity in skew linear groups
type: Item
instance of: scholarly article
title: Hypercentrality and hypercyclicity in skew linear groups
zbMATH Open document ID: 0599.20081
DOI: 10.1007/BF01210709
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: In the paper, we are concerned with skew linear groups G over division rings D, of characteristic \(p\geq 0\), that are locally finite-dimensional over some subfield E, where E is not necessarily central in D. Our main result is to show that locally nilpotent such groups are not necessarily hypercentral (and so locally supersoluble such groups need not be hypercyclic). However, we show that if G is as above such that the maximal unipotent normal subgroup u(G) is trivial or \(p=0\), then G is locally nilpotent if and only if G is hypercentral, but there exists a locally supersoluble such group G that is not hypercyclic.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 16Kxx
zbMATH DE Number: 3966449
zbMATH Keywords: skew linear groups
zbMATH Keywords: division rings
zbMATH Keywords: locally finite-dimensional
zbMATH Keywords: locally nilpotent
zbMATH Keywords: hypercentral
zbMATH Keywords: locally supersoluble
zbMATH Keywords: hypercyclic
zbMATH Keywords: maximal unipotent normal subgroup
author: Iain Stewart
MaRDI profile type: Publication
cites work: Q4145843
cites work: Q3941589
cites work: Supersolubility in Certain Skew Linear Groups
cites work: The paraheight of certain skew linear groups
cites work: Nilpotence in Certain Linear Groups Over Division Rings
cites work: On certain soluble skew-linear groups
cites work: The upper central factors of certain skew-linear groups
cites work: Hyperabelian skew-linear groups
description: scientific article; zbMATH DE number 3966449