# Potentially iterated commutator subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]

## Definition

A subgroup $H$ of a group $G$ is termed a potentially iterated commutator subgroup of $G$ if there exists a group $K$ containing $G$ such that $H$ is an iterated commutator subgroup of $K$, i.e., $H$ is obtained from $K$ through a series of operations that involve taking the commutator of two subgroups. (special cases of this are when $H$ is in the finite part of the derived series or the lower central series of $K$).

## Formalisms

### In terms of the potentially operator

This property is obtained by applying the potentially operator to the property: iterated commutator subgroup
View other properties obtained by applying the potentially operator

## Relation with other properties

### Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Iterated commutator subgroup

### Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions