Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central
type: Item
instance of: scholarly article
title: Finitely generated subnormal subgroups of \(\text{GL}_n(D)\) are central
zbMATH Open document ID: 0947.20032
author: M. Mahdavi-Hezavehi
author: S. Yasamin
author: M. G. Mahmoudi
published in: Journal of Algebra
publication date: 2000-06-07T00:00:00Z
review text: Let \(D\) be a finite-dimensional division algebra. The authors' main result is that every finitely generated subnormal subgroup of the multiplicative group of \(D\) is central. Then there are four corollaries. For example, if \(D\) is infinite, then for every positive integer \(n\), every finitely generated subnormal subgroup of \(\text{GL}(n,D)\) is central. This work extends the study of certain subgroups of \(\text{GL}(n,D)\) carried out in recent years by the first author and his collaborators in various combinations. These earlier papers are listed and, not surprisingly, used in the paper under review.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16K20
zbMATH DE Number: 1429456
zbMATH Keywords: finite-dimensional division algebras
zbMATH Keywords: finitely generated subnormal subgroups
zbMATH Keywords: multiplicative groups
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: jabr.1999.8096
OpenAlex ID: W1985694013
cites work: Normal subgroups of $GL_n(D)$ are not finitely generated
cites work: Maximal subgroups of \(\text{GL}_1(D)\)
cites work: Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
cites work: Q3236717
cites work: Q4266328
cites work: Extension of valuations on derived groups of division rings
cites work: On derived groups of division rings II
DOI: 10.1006/JABR.1999.8096
description: scientific article; zbMATH DE number 1429456