Abstract
In this note, we show that an uncountable locally free group G, and therefore every locally free group, has a free subgroup whose cardinality is the same as that of G. This result directly improves the main result in [4] and establishes the primitivity of group rings of locally free groups.
Funding statement: This research was partially supported by Grants-in-Aid for Scientific Research (KAKEN) under grant no. 26400055.
Acknowledgements
I am grateful to the Editor and an anonymous reviewer for the helpful suggestions that improved the exposition of this paper.
References
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