Subgroup of free group
This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on the ambient 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 subgroup of free group is a subgroup of a free group (i.e., the whole group is free).
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Normal subgroup of free group | a normal subgroup when the whole group is free | |FULL LIST, MORE INFO | ||
| Retract of free group | a retract when the whole group is free | |FULL LIST, MORE INFO | ||
| Free factor of free group | a free factor when the whole group is free | |FULL LIST, MORE INFO | ||
| Characteristic subgroup of free group | a characteristic subgroup when the whole group is free | |FULL LIST, MORE INFO | ||
| Verbal subgroup of free group | a verbal subgroup when the whole group is free | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Free subgroup | freeness is subgroup-closed | |FULL LIST, MORE INFO |