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.

See also 

 Reductive group
 Unipotent group

References 
"Radical of a group", Encyclopaedia of Mathematics

Algebraic groups