Primitive group

Symbol-free definition
A group is said to be primitive if the following equivalent conditions hold:


 * It has a core-free maximal subgroup
 * It possesses a nontrivial faithful primitive group action

Stronger properties

 * Simple group (at least in the case of finite groups)
 * Characteristically simple group
 * 2-transitive group

Weaker properties

 * Quasiprimitive group
 * Innately transitive group

Conjunction with other properties

 * Primitive nilpotent group
 * Primitive solvable group