Permutable subnormal subgroup

Definition
A subgroup of a group is termed a permutable subnormal subgroup if it is both a permutable subgroup and a subnormal subgroup.

Note that since permutable implies subnormal in finite, any permutable subgroup of finite group is a permutable subnormal subgroup.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Permutable 2-subnormal subgroup

Weaker properties

 * Stronger than::Subnormal-permutable subnormal subgroup
 * Stronger than::Subnormal-permutable subgroup
 * Stronger than::Subnormal subgroup
 * Stronger than::Join-transitively subnormal subgroup: