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Abstract. Let W= W(xx,...,Xj)bc any word in thej free generators xx,...,Xj, and suppose that W cannot be expressed in the form W = Vk for V a word and for k an integer with \k\¥" 1. We ask whether the equation f=W has a solution (xx>... ,Xj) = (a,,... ,Oj) €E GJ whenever G is an infinite symmetric group and/is an element in G. We establish an affirmative answer in the case that W(x, y) = xmy" for m and n nonzero integers.

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No abstract