# 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