Abstract: According to the fact that E₁^s,t,* of May spectral sequence is converged to E_A^s,t(Z_p,Z_p) and EE₂^s,t of Adams spectral sequence is converged to stable homotopy groups of sphere π_t-s(S)_p combined with the exact sequence of Ext group induced from the confibration of spectrum. A nonzero element g₀(b₁)⁴ of stable homotopy groups of V(2) is found, and it is a permanent cycle in Adams spectral sequence. With the help of Yonedaproducts, a nonzero element g₀(b₁)⁴γ_s of stable homotopy groups of sphere is obtained.

Key words: Adams spectral sequence, May spectral sequence, stable homotopy group of sphere, sphere spectrum