Freeness is subgroup-closed

This article gives the statement, and possibly proof, of a group property (i.e., free group) satisfying a group metaproperty (i.e., subgroup-closed group property)
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Statement

Every subgroup of a free group is again a free group.

Related facts

• Finitely generated free is not subgroup-closed: A subgroup of a finitely generated free group need not be finitely generated.
• Free abelian is subgroup-closed