A nontrivial product in the stable homotopy groups of spheres

Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Liulevicius described h _i and b _k in Ext* _A ’*(Z_p,Z_p) having bigrading (1, sui— 1) and (2, 2p ^k+1 x(p— 1)), respectively. In this paper we prove that for p ≥ 7, n ≥ 4 and survives to E∞ in the Adams spectral sequence, where q = 2(p — 1).