K-transitivity of a class of block transformations

Let П be an arbitrary finite set, Q(Q) be the collection of all binary quasigroups defined on the set П, and £^F: Qⁿ ^ Qⁿ be the mapping that are implemented by a network £ of width n with one binary operation F E Q(Q). In this paper, we declare a continuation of research related to k-transitivity of the class {£^F : F E Q(H)} in case k ^ 2. Namely, we define conditions for the k-transitivity of the class {£^F : F E Q(Q)}, propose one effective method for verification of network's k-transitivity for all sufficiently large finite sets П, and give parameters of the result of the algorithm for constructing network £ such that the class {£^F : F E Q(H)} is k-transitive.

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