Elementary subgroup of an isotropic reductive group is perfect. (Q2849074)
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scientific article; zbMATH DE number 6208281
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elementary subgroup of an isotropic reductive group is perfect. |
scientific article; zbMATH DE number 6208281 |
Statements
16 September 2013
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reductive groups
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affine group schemes
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elementary subgroup
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Chevalley commutator formula
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Elementary subgroup of an isotropic reductive group is perfect. (English)
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Let \(G\) be an isotropic reductive algebraic group over a commutative ring \(R\). Assume that the elementary subgroup \(E(R)\) of the group of points \(G(R)\) is well defined. Then \(E(R)\) is perfect, except for the well-known case of a split reductive group of type \(C_2\) or \(G_2\).
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