ON TWO NON-TRIVIAL PRODUCTS IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In this paper we consider the convergence of some products in the Adams spectral sequence and show that two products h(0)k(0)h(m) is an element of E(2)(4,2(p1-1)(p1m+2p1+2)), k(0)h(0)h(n)gamma(s) is an element of E(2)(s+4,2(p2-1)(p2n+sp22+(s+1)p2+s)+s-3) permanent cycles in the Adams spectral sequence and converge to two new nontrivial homotopy elements in the stable homotopy groups of spheres pi*S respectively, where p(1) >= 5 is a Prime, p(2) >= 7 is a prime, m >= 3, n >= 4 and 3 <= s < p(2) - 2.