A NEW FAMILY IN THE STABLE HOMOTOPY GROUPS OF SPHERES

Let p be a prime number greater than three. Here, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres π* (S) which is represented by hn hm βs+2 element of Ext^s+4,q [p^n+p^m+(s+2) p+(s+1)]+s A (Zp, Zp) up to a nonzero scalar in the Adams spectral sequence, where n ≥ m + 2 5, 0 ≤ s p − 2, q = 2(p − 1) and βs+2 element of Ext^s+2,q [(s+2) p+(s+1)]+s A (Zp, Zp) as defined by Wang and Zheng.