Radical of an algebraic group

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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 (for a field K) is the subgroup consisting of the matrices with and for .

An algebraic group is called semisimple if its radical is trivial, i.e., consists of the identity element only. The group is semi-simple, for example.

The subgroup of unipotent elements in the radical is called the unipotent radical, it serves to define reductive groups.