Radical of an algebraic group

The radical of an algebraic group is the identity component of its maximal normal solvable subgroup. For example, the radical of the general linear group ${\displaystyle GL_{n}(K)}$ (for a field K) is the subgroup consisting of the matrices ${\displaystyle (a_{ij})}$ with ${\displaystyle a_{11}=\dots =a_{nn}}$ and ${\displaystyle a_{ij}=0}$ for ${\displaystyle i\neq j}$.

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