Locally free group

A group in which every finitely-generated subgroup is free (see Finitely-generated group; Free group). Thus, a countable locally free group is the union of an ascending sequence of free subgroups.

One says that a locally free group has finite rank $n$ if any finite subset of it is contained in a free subgroup of rank $n$, $n$ being the smallest number with this property. The class of locally free groups is closed with respect to taking free products, and the rank of a free product of locally free groups of finite ranks equals the sum of the ranks of the factors.

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