A Nontrivial Homotopy Element of Order p2 Detected by the Classical Adams Spectral Sequence

Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.

Let p be an odd prime. The authors detect a nontrivial element αp of order p2 in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by a0^p-2hl ∈ ExtpA-1pq＋p-2（Z/p,Z/p） in the E2-term of the ASS and meanwhile p. αp is the first periodic element αp.