A nontrivial product in the stable homotopy groups of spheres

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Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Liulevicius described hi and bk in Ext*,A*(Zp, Zp) having bigrading (1, 2pi(p- 1)) and (2, 2pk+1 ×(p - 1)), respectively. In this paper we prove that forp ≥ 7,n≥ 4 and 3 ≤ s < p - 1,h0bn-1γ∈ Exts+3,A pnq+sp2q+(s-1)pq+(s-1)q+s-3(Zp,Zp) survives to E∞ in the Adams spectral sequence, where q = 2(p - 1).
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