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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 3, Pages 591–595
DOI: https://doi.org/10.33048/smzh.2024.65.312 (Mi smj7875) 		 
On regular subgroups in $\mathrm{Lim}(N)$

N. M. Suchkov, A. A. Shlepkin

Siberian Federal University, Krasnoyarsk
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DOI: https://doi.org/10.33048/smzh.2024.65.312
Abstract: Let $G$ be the group of all limited permutations of the set of naturals. We prove that every countable locally finite group is isomorphic to some regular subgroup of $G$. Also, if a regular subgroup $H$ of $G$ contains an element of infinite order then $H$ has a normal infinite cyclic subgroup of finite index.
Keywords: group, limited permutation, locally finite group, regular permutation group.
Funding agency Grant number
Russian Science Foundation 19-71-10017-П
The authors were supported by the Russian Science Foundation (Grant no. 19–71–10017-P)
Received: 16.12.2023
Revised: 16.12.2023
Accepted: 25.01.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 3, Pages 639–643
DOI: https://doi.org/10.1134/S0037446624030121
Document Type: Article
UDC: 512.542
MSC: 35R30
Language: Russian
Citation: N. M. Suchkov, A. A. Shlepkin, “On regular subgroups in $\mathrm{Lim}(N)$”, Sibirsk. Mat. Zh., 65:3 (2024), 591–595; Siberian Math. J., 65:3 (2024), 639–643
Citation in format AMSBIB
\Bibitem{SucShl24}
\by N.~M.~Suchkov, A.~A.~Shlepkin
\paper On~regular subgroups in~$\mathrm{Lim}(N)$
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 3
\pages 591--595
\mathnet{http://mi.mathnet.ru/smj7875}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 3
\pages 639--643
\crossref{https://doi.org/10.1134/S0037446624030121}
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