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 (for a field K) is the subgroup consisting of scalar matrices, i.e. 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.


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