Geodesic
On periodic groups acting freely on abelian groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 136-143
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Let $\pi$ be some set of primes. A periodic group $G$ is called a $\pi$-group if all prime divisors of the order of each of its elements lie in $\pi$. An action of $G$ on a nontrivial group $V$ is called free if, for any $v\in V$ and $g\in G$ such that $vg=v$, either $v=1$ or $g=1$. We describe $\{2,3\}$-groups that can act freely on an abelian group.
Keywords: periodic group, abelian group, free action, local finiteness. 
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A. Kh. Zhurtov; D. V. Lytkina; V. D. Mazurov; A. I. Sozutov. On periodic groups acting freely on abelian groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 136-143. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a12/

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