On locally finite subgroups in $\operatorname{Lim}(N)$

N. M. Suchkov, A. A. Shlepkin

Siberian Federal University, Krasnoyarsk

Abstract: Let $G$ be the group of all limited permutations of the naturals $N$. We prove that every countable locally finite group is isomorphic to a subgroup in $G$.

Keywords: group, limited permutation, locally finite group, regular representation.

UDC: 512.542

MSC: 35R30

Received: 02.03.2023
Revised: 27.04.2023
Accepted: 16.05.2023

DOI: 10.33048/smzh.2023.64.615

 English version: Siberian Mathematical Journal, 2023, 64:6, 1439–1442