The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2 (Q1078329)
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scientific article; zbMATH DE number 3959774
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2 |
scientific article; zbMATH DE number 3959774 |
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The automorphisms of non-defective orthogonal groups \(\Omega _ 8(V)\) and \(O_ 8'(V)\) in characteristic 2 (English)
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1986
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\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 \(O_ 8'(V)\).
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automorphisms
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orthogonal groups
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exceptional automorphisms
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0.87755084
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0.87725914
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0.86054194
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0.85310125
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0.85016114
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