Simple algebraic group

Definition
An algebraic group over a field is said to be simple if it does not contain any proper nontrivial normal connected closed subgroup.

Note that in abstract group-theoretic terms, this does not force the group to be a simple group. However, it does force the group to be a quasisimple group.

Weaker properties

 * Semisimple algebraic group
 * Reductive algebraic group