# Potentially iterated commutator subgroup

From Groupprops

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

## 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 |
---|---|---|---|---|

Normal subgroup | |FULL LIST, MORE INFO | |||

Solvable-quotient normal subgroup | |FULL LIST, MORE INFO |