Normal subgroup-closed group property

Definition
A group property is termed normal subgroup-closed or hereditary to normal subgroups if it satisfies the following equivalent conditions:


 * Whenever a group satisfies the property, so does every normal subgroup of it
 * Whenever a group satisfies the property, so does every 2-subnormal subgroup of it
 * Whenever a group satisfies the property, so does every subnormal subgroup of it

Stronger metaproperties

 * Subgroup-closed group property

Weaker metaproperties

 * Characteristic subgroup-closed group property