Reductive algebraic group

Definition with symbols
A linear algebraic group $$G$$ over a field $$k$$ is said to be reductive if it satisfies the following equivalent conditions:


 * 1) It has no nontrivial normal unipotent connected closed subgroup.
 * 2) Its defining ingredient::unipotent radical is the trivial subgroup.

Stronger properties
Stronger properties of algebraic groups include:


 * Semisimple algebraic group

Weaker properties
Weaker properties of algebraic groups include: