On absolutely irreducible skew linear groups in characteristic zero
type: Item
instance of: scholarly article
title: On absolutely irreducible skew linear groups in characteristic zero
zbMATH Open document ID: 0544.20045
DOI: 10.1007/BF01275567
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Let H be a locally finite normal subgroup of an absolutely irreducible skew linear group. In an earlier paper [J. Lond. Math. Soc., II. Ser. (to appear; Zbl 0545.20040)] we proved that the structure of G modulo the centralizer \(C_ G(H)\) is very restricted, especially in the positive characteristic case. Here we study further the more involved characteristic zero case. The paper quoted above showed that \(G/C_ G(H)\) is metabelian by finite and locally finite but need not be locally-nilpotent by finite. In particular this holds if \(G=H\) so the possibility naturally arises that \(G/HC_ G(H)\) has a simpler structure. We show that \(G/HC_ G(H)\) is abelian by finite and residually finite.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 3865583
zbMATH Keywords: locally finite normal subgroup
zbMATH Keywords: absolutely irreducible skew linear group
zbMATH Keywords: metabelian by finite
zbMATH Keywords: residually finite
author: B. A. F. Wehrfritz
MaRDI profile type: Publication
cites work: Subrings of Noetherian Rings
cites work: Q5675882
cites work: Q5676405
cites work: Locally Finite Normal Subgroups of Absolutely Irreducible Skew Linear Groups
full work available at URL: https://doi.org/10.1007/bf01275567
OpenAlex ID: W2052946278
description: scientific article; zbMATH DE number 3865583