Let $p$ be a prime with $p\geq 7$ and $q=2(p-1)$. In this paper we prove the existence of a nontrivial product of filtration $s+4$ in the stable homotopy groups of spheres. This nontrivial product is shown to be represented up to a nonzero scalar by the product element $\widetilde{\gamma}_{s}b_{n-1}g_{0}\in {Ext}_{\mathcal{A}}^{s+4,(p^n+sp^2+sp+s)q+s-3}(\mathbb{Z}/p,\mathbb{Z}/p)$ in the Adams spectral sequence where $n\geq 2$ and $3\leq s\leq p-1$.
Yu, H., Kou, Y., & Zhao, H. (2015). Detection of a nontrivial element in the stable homotopy groups of spheres. Bulletin of the Iranian Mathematical Society, 41(1), 65-85.
MLA
H. Yu; Y. Kou; H. Zhao. "Detection of a nontrivial element in the stable homotopy groups of spheres". Bulletin of the Iranian Mathematical Society, 41, 1, 2015, 65-85.
HARVARD
Yu, H., Kou, Y., Zhao, H. (2015). 'Detection of a nontrivial element in the stable homotopy groups of spheres', Bulletin of the Iranian Mathematical Society, 41(1), pp. 65-85.
VANCOUVER
Yu, H., Kou, Y., Zhao, H. Detection of a nontrivial element in the stable homotopy groups of spheres. Bulletin of the Iranian Mathematical Society, 2015; 41(1): 65-85.