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.
@article{TIMM_2013_19_3_a12,
author = {A. Kh. Zhurtov and D. V. Lytkina and V. D. Mazurov and A. I. Sozutov},
title = {On periodic groups acting freely on abelian groups},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {136--143},
publisher = {mathdoc},
volume = {19},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a12/}
}
TY - JOUR AU - A. Kh. Zhurtov AU - D. V. Lytkina AU - V. D. Mazurov AU - A. I. Sozutov TI - On periodic groups acting freely on abelian groups JO - Trudy Instituta matematiki i mehaniki PY - 2013 SP - 136 EP - 143 VL - 19 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a12/ LA - ru ID - TIMM_2013_19_3_a12 ER -
%0 Journal Article %A A. Kh. Zhurtov %A D. V. Lytkina %A V. D. Mazurov %A A. I. Sozutov %T On periodic groups acting freely on abelian groups %J Trudy Instituta matematiki i mehaniki %D 2013 %P 136-143 %V 19 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a12/ %G ru %F TIMM_2013_19_3_a12
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/