Subnormal-permutable subnormal subgroup
From Groupprops
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
Contents
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.
Relation with other properties
Stronger properties
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
- Subnormal subgroup
