Group in which every pronormal subgroup is normal

Symbol-free definition
A group in which every pronormal subgroup is normal is a group with the property that any defining ingredient::pronormal subgroup of the group is a defining ingredient::normal subgroup.

Stronger properties

 * Weaker than::Nilpotent group
 * Weaker than::Group in which every subgroup is subnormal
 * Weaker than::Group satisfying normalizer condition
 * Weaker than::Locally nilpotent group

Facts
For a finite group, every pronormal subgroup being normal is equivalent to the group being a finite nilpotent group.