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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

Contents

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 Retract of free group|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