Abstract
In 2001, J. Lin detected a non-trivial element in the stable homotopy group of the sphere spectrum S for at the prime greater than three. In the stable homotopy group of the Smith–Toda spectrum , X. Liu constructed an essential element for at the prime greater than three. Let denote the Spanier–Whitehead dual of the generator , which defines the -element . Let . In this paper, we show that the composite maps and are non-trivial, where and . In the Adams–Novikov spectral sequence, the maps and are represented by and , respectively. Here denotes the well-known element in .
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