A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres

In this paper, some groups Exts,tA(Zp,Zp) with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres .pnq+(s+3)pq+(s+1)q.5S which is represented (up to a nonzero scalar) by \ifmmode\expandafter\else~\expandafter\~\fi.s+2b0hn.Exts+5,pnq+(s+3)pq+(s+1)q+sA(Zp,Zp) in the Adams spectral sequence, where p . 5 is a prime number, n . 3, 0 . s < p . 3, q = 2(p . 1).