Abstract
A group acting on an abelian group is finite provided that it is generated by a class of conjugate elements such that every two elements of the class generate a finite subgroup that acts freely.
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Zhurtov, A.K. On a Group Acting Locally Freely on an Abelian Group. Siberian Mathematical Journal 44, 275–277 (2003). https://doi.org/10.1023/A:1022932820511
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DOI: https://doi.org/10.1023/A:1022932820511