TITLE: Virtually free, torsion-free, and locally free groups
QUESTION [11 upvotes]: A well-known theorem of Stallings says that 
any finitely generated virtually free torsion-free group is free.

Is this true without `finitely generated' condition?

In other words,

is every locally free virtually free group free?

REPLY [10 votes]: 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:

Let $G$ be a torsion-free group. If $G$ has a free subgroup of finite index, then $G$ is free. 

Here's the paper (apparently not behind a paywall).