Some new families of filtration five in the stable homotopy of spheres

This study proves a general result on convergence of 2x ∈ Exts+2, tq+2q+1A(Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q−4S which is represented in the Adams spectral sequence by 2fn, 2f′n, 2huhmhn ∈ Ext5, tq+2q+1A(Zp, Zp) with tq = pn+1q+2pnq, 2pn+1q+pnq, puq+pmq+pnq, respectively, where 2 ∈ Ext2,2q+1a(Zp,Zp),fn ∈ Ext3,pn+1 q+2pnqA (Zp,Zp), f′n ∈ Ext3,2pn+1 q+pnqA (Zp,Zp), hn ∈ Ext1, pnqA (Zp,Zp) and p ≥ 5 is a prime, q = 2(p − 1),n ≥ 2.