Some Result about a Product of Conjugate Cycles
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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