Subnormal-permutable subnormal subgroup

Definition
A subgroup of a group is termed a subnormal-permutable subnormal subgroup if it is a subnormal subgroup as well as a subnormal-permutable subgroup: it permutes with every subnormal subgroup of the group.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Perfect subnormal subgroup

Weaker properties

 * Stronger than::Permutable subnormal subgroup (for a finite group, every permutable subgroup is subnormal, so any permutable subgroup is a subnormal-permutable subnormal subgroup)
 * Stronger than::Join-transitively subnormal subgroup
 * Stronger than::Subnormal subgroup