Torsion bounds of loop spaces and suspensions

The k-invariants k(n) in the Postnikov decomposition of a finite type connected H-space X are known to be torsion elements, that is, there exist numbers N-n(X) with N-n (X) (.) k(n) = 0 for n greater than or equal to 2. We describe classes of H-spaces for which N-n (X) = N-n can be chosen to be the same number for all X in the class. Dually the boundary invariants beta(n) of a finite type simply connected co-H-space Y satisfy M-n(Y) (.) beta(n) = 0. We describe classes of co-H-spaces for which M-n(Y) = M-n can be chosen to be the same number for all Y in the class.