The maximality of monomial subgroups of linear groups over division rings
type: Item
instance of: scholarly article
title: The maximality of monomial subgroups of linear groups over division rings
zbMATH Open document ID: 0684.20037
DOI: 10.1016/0021-8693(89)90270-6
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: The author proves that the full monomial group is a maximal subgroup of GL(n,D), where D is a division ring and \(n\geq 2\) an integer, except for those cases that are already exceptions when D is commutative (these are fully listed). The author then considers the corresponding problem for SL(n,D). This too he settles, except that if D is infinite, commutative and of characteristic not 2 he needs to assume that D has enough squares. The proofs look elementary, but the calculations are fierce.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 4120409
zbMATH Keywords: linear groups over division rings
zbMATH Keywords: monomial group
zbMATH Keywords: maximal subgroup
author: Shangzhi Li
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90270-6
OpenAlex ID: W2090053471
cites work: On the maximal subgroups of the finite classical groups
cites work: Some maximal subgroups of \(PSL(n,q)\), \(n\geq 3,\;q=2^r\)
cites work: Some Maximal Subgroups of Certain Projective Unimodular Groups
cites work: Maximal subgroups of the finite orthogonal and unitary groups stabilizing anisotropic subspaces
cites work: Some Properties of a Sfield
cites work: Q5798860
cites work: Q3251484
description: scientific article; zbMATH DE number 4120409