The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2
\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 \(O_ 8'(V)\).
scientific article; zbMATH DE number 3959774