Elementary subgroup of an isotropic reductive group is perfect
Elementary subgroup of an isotropic reductive group is perfect
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 $G_2$.