On locally finite subgroups in \(\operatorname{Lim}(N) \) (Q6179776)

Let \(N\) be the set of natural numbers and \(S(N)\) be the group of all permutations of \(N\). A permutation \(g \in S(N)\) is limited if \(\omega(g)=\max_{\alpha \in N} |\alpha - \alpha^g| < \infty\). All such permutations constitute the group \(G =\mathrm{Lim}(N)\). It is proved that a universal countable locally finite Hall group is isomorphic to a regular subgroup of \(\mathrm{Lim}(N)\).