Derived subgroup of an affine algebraic group
= Derived subgroup of an affine algebraic group
The derived subgroup $[G,G]$ is the closed algebraic subgroup generated by the commutators $xyx^{-1}y^{-1}$. If $G$ is connected, images of finite products of commutators are connected and their closures stabilize by dimension, which shows that $[G,G]$ is connected.