Wreath products of the groups of monotone permutations

We introduce the concept of wreath product of the $m$-groups of permutations and prove that an $m$-transitive group of permutations with an m-congruence is embeddable into the wreath product of the suitable $m$-transitive $m$-groups of permutations. This implies that an arbitrary $m$-transitive group in the product of two varieties of $m$-groups embeds into the wreath product of the suitable $m$-transitive groups of these varieties.