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A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial

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Product of standard parabolic subgroups

Consider a quasi-split reductive group $G$ over a field $k$. Let $B$ be a Borel subgroup of $G$, and let $P, Q$ be two parabolic subgroups of $G$ that contain $B$. Is the product set $PQ = \{xy| x \in …