@article { author = {Yu, H. and Kou, Y. and Zhao, H.}, title = {Detection of a nontrivial element in the stable homotopy groups of spheres}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {41}, number = {1}, pages = {65-85}, year = {2015}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, 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 $3\leq s\leq p-1$‎. }, keywords = {‎S‎table homotopy groups of sphere‎,‎Adams spectral sequence‎,‎May spectral sequence}, url = {http://bims.iranjournals.ir/article_590.html}, eprint = {http://bims.iranjournals.ir/article_590_85ba0e058a40f200e803319d8a76cec7.pdf} }