An infinite family in ${}\sb 2\pi\sp {\rm s}\sb *$ at Adams filtration seven

Abstract

We prove the family $\{ h_i^2{h_3}{d_1}\}$ in $\operatorname {Ext}_A^{7,\ast }({\mathbb {Z}_2},{\mathbb {Z}_2})$ detects homotopy elements in the $2$-adic stable homotopy of spheres $_2\pi _{\ast }^S$ where $A$ is the $\bmod \;2$ Steenrod algebra.