Quasiprimitive group

Symbol-free definition
A group is said to be quasiprimitive if it satisfies the following equivalent conditions:


 * It possesses a faithful group action such that the restriction to every nontrivial normal subgroup is transitive
 * It possesses a strongly contranormal subgroup, viz a subgroup whose product with every nontrivial normal subgroup is the whole group

Stronger properties

 * Primitive group
 * Doubly transitive group

Weaker properties

 * Innately transitive group