# Retract of free group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: retract with a group property imposed on theambient group: free group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A **retract of free group** is a retract of a free group.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Free factor of free group | retract not implies free factor in free group | |FULL LIST, MORE INFO |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Subgroup of free group | |FULL LIST, MORE INFO |