A well-known theorem of Stallings says that 


*any finitely generated virtually free torsion-free group is free.*



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> Is this true without **`finitely generated'** condition?
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In other words,



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> is every locally free virtually free group free?
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Virtually free, torsion-free, and locally free groups
This is Theorem B of Swan's famous paper *Groups of cohomological dimension one*, in which he removes the 'finitely generated' hypothesis from Stallings' theorem. Theorem B states:



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> Let $G$ be a torsion-free group. If $G$ has a free subgroup of finite index, then $G$ is free. 
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[Here](https://dx.doi.org/10.1016%2F0021-8693%2869%2990030-1)'s the paper (apparently not behind a paywall).


