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This article is cited in 2 scientific papers (total in 2 papers)
Even permutations not representable in the form of a product of two permutations of given order
V. G. Bardakov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
The paper gives a description the permutations from the alternating group An that, for a given positive integer k⩾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 set Qk such that, for each n from Qk, the group An 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 order k.
Received: 27.06.1995
Citation:
V. G. Bardakov, “Even permutations not representable in the form of a product of two permutations of given order”, Mat. Zametki, 62:2 (1997), 169–177; Math. Notes, 62:2 (1997), 141–147
Linking options:
https://www.mathnet.ru/eng/mzm1602https://doi.org/10.4213/mzm1602 https://www.mathnet.ru/eng/mzm/v62/i2/p169
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Abstract page: | 460 | Full-text PDF : | 269 | References: | 58 | First page: | 1 |
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