PS-group

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


 * Every max-core (viz the normal core of a maximal subgroup) is a maximal normal subgroup
 * Every quotient of the group which is a primitive group is in fact a simple group

Definition with symbols
A group $$G$$ is said to be a PS-group if it satisfies the following equivalent conditions:


 * For any maximal subgroup $$M \le G$$, the normal core of $$M$$ is a maximal normal subgroup of $$G$$
 * Given any quotient map from $$G$$ to a primitive group, the image of the map is in fact a simple group.

Stronger properties

 * Simple group
 * Nilpotent group