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 Ext A ∗ 3 , ∗ ( Z / p , Z / p ) 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 d 2 ( h i + 1 ) = a 0 b i and the matrix Massey products, we determined the secondary Adams differentials on the generators of N.