On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices
type: Item
instance of: scholarly article
title: On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices
zbMATH Open document ID: 0881.20023
DOI: 10.1016/S0022-4049(96)00051-5
published in: Journal of Pure and Applied Algebra
publication date: 1998-02-22T00:00:00Z
review text: Let \(T\) be a division algebra and \(\Gamma=\text{SL}_n(T)\) with \(n\geq 3\). The author proves that, for any subgroup \(H\) of \(\Gamma\) containing all diagonal matrices, there exists a unique \(D\)-net \(\sigma\) such that \(\Gamma(\sigma)\leq H\leq N_\Gamma(\sigma)\) where \(\Gamma(\sigma)\) is the \(D\)-net subgroup corresponding to \(\sigma\).
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1076650
zbMATH Keywords: special linear groups
zbMATH Keywords: division algebras
zbMATH Keywords: diagonal matrices
zbMATH Keywords: net subgroups
author: Bùi Xuân Hải
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1076650