Let be a prime greater than three. In the –local stable homotopy groups of spheres, R L Cohen constructed the infinite –element of order . In the stable homotopy group of the Smith–Toda spectrum , X Liu constructed an essential element for . Let denote the Spanier–Whitehead dual of the generator , which defines the –element . Let . In this paper, we show that the composite of R L Cohen’s –element with is nontrivial, where and . As a corollary, is also nontrivial for .
"On R L Cohen's $\zeta$–element." Algebr. Geom. Topol. 11 (3) 1709 - 1735, 2011. https://doi.org/10.2140/agt.2011.11.1709