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On regular subgroups in $\mathrm{Lim}(N)$
N. M. Suchkov, A. A. Shlepkin Siberian Federal University, Krasnoyarsk
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.
Received: 16.12.2023 Revised: 16.12.2023 Accepted: 25.01.2024
Citation:
N. M. Suchkov, A. A. Shlepkin, “On regular subgroups in $\mathrm{Lim}(N)$”, Sibirsk. Mat. Zh., 65:3 (2024), 591–595
Linking options:
https://www.mathnet.ru/eng/smj7875 https://www.mathnet.ru/eng/smj/v65/i3/p591
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Abstract page: | 71 | Full-text PDF : | 3 | References: | 24 | First page: | 13 |
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