Homotopy decompositions of looped co-H spaces of low-rank

Let p be an odd prime. For a kind of p-local co-H space Y of low-rank, it is shown in this paper that ΩY has ΩΣkY as a product factor for a sequence of k which admits an exponential growth. The result appears as a result of the application of recently developed technique for functorial decompositions of looped co-H spaces via the functorial coalgebra decompositions of tensor algebras.