  Let X be a countably infinite set, and let f, g, and h be any three injective
self-maps of X, each having at least one infinite cycle. (For instance, this
holds if f, g, and h are not bijections.) We show that there are permutations a
and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We
also prove a version of this statement that holds for infinite sets X that are
not necessarily countable. This generalizes results of Droste and Ore about
permutations.
