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Some Result about a Product of Conjugate Cycles | ||
| Journal of Al-Nahrain University - Science | ||
| Article 1, Volume 14, Issue 4, 2011, Pages 158-165 | ||
| Abstract | ||
| The aim of this paper is to give a generalization of the theorem that, for n 5, every even permutation defined on n symbols is commutator a b a-1 b-1 of even permutations a and b. In particular, [3n/4] L n is shown to be the necessary and sufficient condition on L, in order that every even permutation defined on n 5 symbols can be expressed as a product of two cycles, each of length L. Results follow, including every odd permutation is a product of a cycle of length L and a cycle of length L + 1. | ||
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