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 scalar matrices, i.e. matrices
An algebraic group is called semisimple if its radical is trivial, i.e., consists of the identity element only.
The subgroup of unipotent elements in the radical is called the unipotent radical, it serves to define reductive groups.
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