Determination of the order of the P-image by Toda brackets

The purpose of this talk is to try to determine the orders of Whitehead products [ι_n,α] for n ≥ k + 2,k ≤ 24, where ι_n is of the identity class of an n-sphere Sⁿ and α is an element of the 2-primary components of the k-stem of the homotopy groups of Sⁿ. We use the classical methods of homotopy theory, i.e. mainly the results of Kervaire, Mahowald, Mimura, Nomura, Oda and Toda.