# Detection of a nontrivial element in the stable homotopy groups of spheres

Document Type : Research Paper

Authors

South China Normal University

Abstract

‎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 $3\leq s\leq p-1$‎.

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### History

• Receive Date: 24 September 2013
• Revise Date: 11 December 2013
• Accept Date: 12 December 2013
• First Publish Date: 01 February 2015