On normal subgroups of limited permutation groups

In this paper we describe the commutator subgroups of limited permutation groups $F=\mathrm{Lim}(Z)$, $G=\mathrm{Lim}(N)$ of the sets of integers $Z$ and natural numbers $N$. The connection between a complite dispersion subsets of $N$ and local finite normal subgroups of $G$ is investigated.