A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES*

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres πt-6S which is represented by in the Adams spectral sequence, where t = 2pn(p - 1) + 6(p2 + p + 1)(p - 1) and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s + 6 in the stable homotopy groups of spheres πt1-s-6S which is represented by in the Adams spectral sequence, where n ≥ 4, 0 ≤ s < p-4, t1 = 2pn(p - 1) + 2(p - 1)((s + 3)p2 + (s + 3)p + (s + 3)) + s.