The secondary differentials on the third line of the Adams spectral sequence

Let p⩾5 be an odd prime. In this paper the third line of the Adams spectral sequence (ASS) is divided into the direct sum of three sub-modules, say T, C and N. We proved that the generators of T are in the images of the Thom map, and the generators of C can survive to some low dimensional elements of the Adams–Novikov spectral sequence (ANSS). Thus they have trivial secondary Adams differentials. By computing the Adams differentials induced by d2(hi+1)=a0bi and the matrix Massey products, we determined the secondary Adams differentials on the generators of N.