Some Result about a Product of Conjugate Cycles

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.