Subnormal-permutable subnormal subgroup

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

Definition

A subgroup of a group is termed a subnormal-permutable subnormal subgroup if it is a subnormal subgroup and it permutes with every subnormal subgroup of the group.

Relation with other properties

Stronger properties

• Normal subgroup
• Perfect subnormal subgroup

Weaker properties

• Permutable subnormal subgroup (for a finite group, every permutable subgroup is subnormal, so any permutable subgroup is a subnormal-permutable subnormal subgroup)
• Join-transitively subnormal subgroup