# Subgroup realizable as the commutator of the whole group and a subgroup

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 **realizable as the commutator of the whole group and a subgroup** if it can be realized as the commutator of the whole group and a subgroup.

## Relation with other properties

### Stronger properties

- Perfect normal subgroup
- Member of the (finite) lower central series