Permutable subnormal subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutable subgroup and subnormal subgroup
View other subgroup property conjunctions | view all subgroup properties

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.

Relation with other properties

Stronger properties

• Normal subgroup
• Permutable 2-subnormal subgroup

Weaker properties

• Subnormal-permutable subnormal subgroup
• Subnormal-permutable subgroup
• Subnormal subgroup
• Join-transitively subnormal subgroup: For full proof, refer: Subnormality is permuting join-closed