On Regular Subgroups in $ \operatorname{Lim}(N) $

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.