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.