Locally free group
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.
|||A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)|
Locally free group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locally_free_group&oldid=39697