# PS-group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### 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 is said to be a **PS-group** if it satisfies the following equivalent conditions:

- For any maximal subgroup , the normal core of is a maximal normal subgroup of
- Given any quotient map from to a primitive group, the image of the map is in fact a simple group.