Abstract
The paper gives a description the permutations from the alternating groupA n that, for a given positive integerk≥4, cannot be presented as a product of two permutations each of which contains only cycles of lengths 1 and 4 in the expansion into independent cycles. We construct a setQ k such that, for eachn fromQ k , the groupA n contains a permutation not representable in the above form. We give answers to two questions of Brenner and Evans on the representability of even permutations in the form of a product of two permutations of a given orderk.
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References
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Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 169–177, August, 1997.
Translated by A. I. Shetern
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Bardakov, V.G. Even permutations not representable in the form of a product of two permutations of given order. Math Notes 62, 141–147 (1997). https://doi.org/10.1007/BF02355902
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DOI: https://doi.org/10.1007/BF02355902