1
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R China
2
Mathematics and Information Science College,Hebei Normal University, 050016,Shijiazhuang, P. R. China
Abstract
Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq s Ext}_A^{s+2,q[(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ was defined by X. Wang and Q. Zheng.
