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Normal subgroups and there properties for finite and infinite iterated wreathproducts $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded.The special classes of normal subgroups and there orders are investigated.Special classes of normal subgroups are investigated and their generators arefound and presented in the form of Kaloujnine tables. Inverse limit of wreathproduct of permutation groups is found.

Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups