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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 136–143
(Mi timm970)
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This article is cited in 11 scientific papers (total in 11 papers)
On periodic groups acting freely on abelian groups
A. Kh. Zhurtova, D. V. Lytkinab, V. D. Mazurov, A. I. Sozutovc a Kabardino-Balkar State University
b Siberian State University of Telecommunications and Informatics
c Siberian Federal University
Abstract:
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.
Received: 28.01.2013
Citation:
A. Kh. Zhurtov, D. V. Lytkina, V. D. Mazurov, A. I. Sozutov, “On periodic groups acting freely on abelian groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 136–143; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S209–S215
Linking options:
https://www.mathnet.ru/eng/timm970 https://www.mathnet.ru/eng/timm/v19/i3/p136
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Abstract page: | 391 | Full-text PDF : | 99 | References: | 55 | First page: | 8 |
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