Overgroups of SU(n,K,f) or \(\Omega\) (n,K,Q) in GL(n,K)
type: Item
instance of: scholarly article
title: Overgroups of SU(n,K,f) or \(\Omega\) (n,K,Q) in GL(n,K)
zbMATH Open document ID: 0694.20031
DOI: 10.1007/BF00181331
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: Let K be a division ring with involution, f an isotropic hermitian or skew-hermitian even (trace-valued) form on an n-dimensional left K-vector space, \(n\geq 3\), \(N=SU(n,K,f)\) the subgroup of the unitary group generated by transvections. Theorem 1 asserts that every subgroup X of GL(n,K) containing N either normalizes N or contains SL(n,K). Theorem 2 asserts a similar result for orthogonal groups over commutative K (which differ from the corresponding unitary groups in the case \(2K=0)\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4136226
zbMATH Keywords: division ring with involution
zbMATH Keywords: unitary group
zbMATH Keywords: transvections
zbMATH Keywords: orthogonal groups
author: Shangzhi Li
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181331
OpenAlex ID: W2003779624
description: scientific article; zbMATH DE number 4136226