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.

UDC: 512.542

MSC: 35R30

Received: 16.12.2023
Revised: 16.12.2023
Accepted: 25.01.2024

DOI: 10.33048/smzh.2024.65.312

 English version: Siberian Mathematical Journal, 2024, 65:3, 639–643