The fact that every subgroup of a free group is free follows quite naturally from the theory of covering spaces applied to graphs.
Is it also possible to proof this theorem without topology, by using only algebraic considerations?
2026-03-28 05:22:58.1774675378
Proof that every subgroup of a free group is free (without using algebraic topology)
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Of course. You can find such a proof in all textbook on Theory of Groups, e.g.:
Lyndon, Schupp. Combinatorial Group Theory
Magnus, Karrass, Solitar. Combinatorial Group Theory
M.Hall. Theory of groups
A.Kurosh. Theory of groups