A nontrivial homotopy element of order p2 detected by the classical Adams spectral sequence

Abstract

Let p be an odd prime. The authors detect a nontrivial element a p of order p2 in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by $$a_0^{p - 2} h_1 \in Ext_A^{p - 1,pq + p - 2} (\mathbb{Z}/p,\mathbb{Z}/p)$$ in the E2-term of the ASS and meanwhile p · a p is the first periodic element α p .