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Automorphism groups of vector groups over a field of positive characteristic. (English) Zbl 1171.20315

Summary: We define elementary automorphisms of the \(n\)-dimensional vector group over an algebraically closed field of positive characteristic and show that they generate the automorphism group of the vector group. We also give a necessary and sufficient computational condition for a \(d\)-tuple of \(p\)-polynomials to be a component of an \(n\)-tuple of \(p\)-polynomials defining an automorphism of the vector group.

MSC:

20G15 Linear algebraic groups over arbitrary fields
20F28 Automorphism groups of groups
14L35 Classical groups (algebro-geometric aspects)
15A03 Vector spaces, linear dependence, rank, lineability
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