Centralizer of the elementary subgroup of an isotropic reductive group. (Q357772)

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scientific article; zbMATH DE number 6198104
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Centralizer of the elementary subgroup of an isotropic reductive group.
scientific article; zbMATH DE number 6198104

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    Centralizer of the elementary subgroup of an isotropic reductive group. (English)
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    13 August 2013
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    Let \(G\) be an isotropic reductive algebraic group over a commutative ring \(R\) having a strictly proper parabolic subgroup \(P\). Assume that for any maximal ideal \(M\) of \(R\) all irreducible components of the relative root system of \(G_{R_M}\) are of rank \(\geq 2\). Let \(E_P(R)\) be the subgroup of \(G(R)\) generated by the \(R\)-points of the unipotent radicals of \(P\) and of an opposite parabolic subgroup. Then the centralizer of \(E_P(R) \) is the center of \(G(R)\).
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    isotropic reductive algebraic groups over rings
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    parabolic subgroups
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    unipotent radicals
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    centralizers
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    center
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