The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2
type: Item
instance of: scholarly article
title: The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2
zbMATH Open document ID: 0596.20038
published in: Chinese Annals of Mathematics. Series B
publication date: 1986-01-01T00:00:00Z
review text: \textit{E. A. Connors} [J. Number Theory 5, 477-501 (1973; Zbl 0275.20091)] determined the automorphisms of non-defective n-dimensional (n\(\geq 10)\) orthogonal groups \(\Omega_ n(V)\) and \(O_ n'(V)\) in characteristic 2. In 1983 the author lowered the bound on the dimension from ten to six, but excluding the case \(n=8\), because \(\Omega_ 8(V)\) and \(O_ 8'(V)\) have exceptional automorphisms. In this paper, under the assumption that the ground field \(F\neq {\mathbb{F}}_ 2\), the author proves that every exceptional automorphism of \(O_ 8'(V)\) has exactly one of the forms: \(\phi_ i\cdot \Phi_ g\) or \(f_ 2\cdot \Phi_ g\) where \(\Phi_ g\) is standard, and \(\phi_ 1\) and \(\phi_ 2\) are the automorphisms induced by the triality principle. Every exceptional automorphism of \(\Omega_ 8(V)\) is the restriction of a unique exceptional automorphism of \(O_ 8'(V)\).
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 3959774
zbMATH Keywords: automorphisms
zbMATH Keywords: orthogonal groups
zbMATH Keywords: exceptional automorphisms
author: Fu-an Li
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3959774