Expansion of even permutations into two factors of the given cyclic structure

V. G. Bardakov


We prove Brenner-Evans' conjecture that, for any natural numbers k ≥ 4 and m ≥ 1, any even permutation of the group Akm is a product of two permutations, each of them is expanded into a product of m independent cycles of length k. It is known that this assertion is incorrect for k = 2, 3.

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Discrete Mathematics and Applications provides the latest information on the development of discrete mathematics in Russia to a world-wide readership. The journal covers various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.