Subgroups of the special linear group containing the diagonal subgroup
type: Item
instance of: scholarly article
title: Subgroups of the special linear group containing the diagonal subgroup
zbMATH Open document ID: 0715.20028
DOI: 10.1016/0021-8693(90)90263-N
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: In the paper subgroups of the special linear group \(SL_ 2(K)\) of degree 2 over a field K, containing the subgroup D of all diagonal matrices are described. If char \(K\neq 2\), \(| K| >11\) and \(D<F\leq SL_ 2(K)\) then F is one of the following: the subgroup M of all monomial matrices, the subgroup U of upper triangular matrices, the subgroup L of all lower triangular matrices or \(SL_ 2(K)\) (Theorem 1). If char K\(=2\), \(K\neq GF(2)\) and \(D<F\leq SL_ 2(K)\) then one of the following occurs: \(F\leq U\), \(F\leq L\) or \(M\leq F\) (Theorem 2).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4177380
zbMATH Keywords: subgroups
zbMATH Keywords: special linear group
zbMATH Keywords: diagonal matrices
zbMATH Keywords: monomial matrices
zbMATH Keywords: upper triangular matrices
author: Oliver King
reviewed by: V. Ya. Bloshchitsyn
MaRDI profile type: Publication
cites work: On the maximality of the orthogonal groups in the symplectic groups in characteristic two
cites work: On some maximal subgroups of the classical groups
cites work: On subgroups of the special linear group containing the special orthogonal group
cites work: Subgroups of the general symplectic group containing the group of diagonal matrices
full work available at URL: 0021-8693(90)90263-n
OpenAlex ID: W1972480124
description: scientific article; zbMATH DE number 4177380