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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 136–143 (Mi timm970)

This article is cited in 11 scientific papers (total in 11 papers)

On periodic groups acting freely on abelian groups

A. Kh. Zhurtov^a, D. V. Lytkina^b, V. D. Mazurov, A. I. Sozutov^c

^a Kabardino-Balkar State University
^b Siberian State University of Telecommunications and Informatics
^c Siberian Federal University

Full-text PDF (170 kB) Citations (11)

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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

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 285, Issue 1, Pages S209–S215
DOI: https://doi.org/10.1134/S008154381405023X

Bibliographic databases:

Document Type: Article

UDC: 512.5

Language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/timm970

https://www.mathnet.ru/eng/timm/v19/i3/p136

This publication is cited in the following 11 articles:

Shi Wujie, “Quantitative characterization of finite simple groups”, Sci. Sin.-Math., 53:7 (2023), 931
B. E. Durakov, A. I. Sozutov, “On groups with involutions saturated by finite Frobenius groups”, Siberian Math. J., 63:6 (2022), 1075–1082
A. I. Sozutov, “Groups Saturated with Finite Frobenius Groups”, Math. Notes, 109:2 (2021), 270–279
N. E. Mirzakhanyan, H. V. Piliposyan, “On a question of A. Sozutov”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:2 (2018), 88–92
A. R. Chekhlov, “Abelian groups with monomorphisms invariant with respect to epimorphisms”, Russian Math. (Iz. VUZ), 62:12 (2018), 74–80
S. I. Adian, V. S. Atabekyan, “Central extensions of free periodic groups”, Sb. Math., 209:12 (2018), 1677–1689
A. I. Sozutov, E. B. Durakov, “On groups with a Frobenius element”, Siberian Math. J., 59:5 (2018), 938–946
A. M. Popov, A. I. Sozutov, “On groups with Frobenius elements”, Siberian Math. J., 56:2 (2015), 352–357
Daria V. Lytkina, Victor D. Mazurov, “Groups with given element orders”, Zhurn. SFU. Ser. Matem. i fiz., 7:2 (2014), 191–203
D. V. Lytkina, V. D. Mazurov, “On $\{2,3\}$-groups without elements of order 6”, Siberian Math. J., 55:6 (2014), 1098–1104
D. V. Lytkina, V. D. Mazurov, “$\{2,3\}$-groups with no elements of order 6”, Algebra and Logic, 53:6 (2015), 463–470

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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