Semisimple algebraic group

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


 * 1) It has no nontrivial normal solvable connected closed subgroup.
 * 2) Its radical is the trivial subgroup.

Stronger properties
Stronger properties of algebraic groups include:


 * Weaker than::Simple algebraic group

Weaker properties
Weaker properties of algebraic groups include:


 * Stronger than::Reductive algebraic group