Group in which every normal subgroup is fully invariant

Symbol-free definition
A group in which every normal subgroup is fully characteristic or group in which every normal subgroup is fully characteristic is a group with the property that every normal subgroup of the group is fully invariant in it.

Formalisms
The property can be expressed as the collapse of the following subgroup properties: normal subgroup = fully invariant subgroup

Stronger properties

 * Weaker than::Simple group

Weaker properties

 * Stronger than::Group in which every normal subgroup is characteristic
 * Stronger than::Group in which every characteristic subgroup is fully invariant