On Nontriviality of a Product in the Classical Adams Spectral Sequence

Abstract

Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.