Some products involving the fourth Greek letter family element δs in the Adams spectral sequence

Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E2 -term of the Adams spectral sequence, Ext *,* A (Zp, Zp) . In this paper we prove that in the cohomology of A , the product k0hn δs+4 element of Ext s+7,t(s,n)+s A (Zp, Zp), is nontrivial for n ≥ 5, and trivial for n =3, 4, where δs+4 is actually α(4) s+4 described by Wang and Zheng, p ≥ 11, 0 ≤ s p−4 and t(s, n)= 2(p−1)[(s+2)+(s+4)p+(s+3)p 2 +(s+4)p 3 +p n].