A (B)n-Related Family of Homotopy Elements in the Stable Homotopy of Spheres

To determine the stable homotopy groups of spheres π* (S) is one of the central problems in homotopy theory.Let p be a prime greater than 5.The authors make use of the May spectral sequence and the Adams spectral sequence to prove the existence of a (B)n-related family of homotopy elements,β1ωnγs,in the stable homotopy groups of spheres,where n ＞ 3,3 ≤ s ＜ p-2 and the (B)n-element was detected by X.Liu.