# 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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