Locally free group

From Encyclopedia of Mathematics
Jump to: navigation, search

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.


[1] A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)
How to Cite This Entry:
Locally free group. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.L. Shmel'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article