Permutable subgroup of normal subgroup

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: permutable subgroup and normal subgroup
View other such compositions|View all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a permutable subgroup of normal subgroup if it is expressible as a permutable subgroup of a normal subgroup of the whole group.

Relation with other properties

Stronger properties

• Normal subgroup
• Permutable subgroup
• 2-subnormal subgroup

Weaker properties

• Automorph-permutable subgroup of normal subgroup
• Conjugate-permutable subgroup
• Subnormal subgroup in case of a finite group.