# Free factor of free group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: free factor 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

## Definition

A **free factor of free group** is a free factor where the whole group is a free group.

## Relation with other properties

### Weaker properties

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

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

Free factor | |FULL LIST, MORE INFO |