Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups

Analyses the abstract structure of algebraic groups over an algebraically closed field $K$. For $K$ of characteristic zero and $G$ a given connected affine algebraic $\overline{\mathbb Q}$-group, the theorem describes the affine algebraic $\overline{\mathbb Q} $-groups $H$ such that the groups $H(K)$ and $G(K)$ are isomorphic as abstract groups.