# Subgroup contained in the Baer norm

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Contents

## Definition

A subgroup of a group is termed a **subgroup contained in the Baer norm** if it satisfies the following equivalent conditions:

- It is contained in the Baer norm of the whole group.
- It normalizes every subgroup of the whole group.

## Formalisms

### In terms of the subgroup-defining function containment operator

This property is obtained by applying the subgroup-defining function containment operator to the property: Baer norm

View other properties obtained by applying the subgroup-defining function containment operator

## Relation with other properties

### Weaker properties

- Permutable subgroup: Also related:
- 2-subnormal subgroup: Also related:
- Permutable 2-subnormal subgroup