Elementary subgroup of an isotropic reductive group is perfect

preprint2010arXivOpen access

Abstract

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that the elementary subgroup E(R) of group of points G(R) is correctly defined. Then E(R) is perfect, except for the well-known cases of a split reductive group of type C_2 or G_2.

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