Abstract
In this paper, we re-compute the cohomology of the Morava stabilizer algebra $S(3)$ [12, 16]. As an application, we show that for $p \geq 7$, if $s\not \equiv 0, \pm 1 \,\, mod \,(p) $, $n\not \equiv 1 \,\, mod\, 3$, $n>1$, then $\zeta_n\gamma_s$ is a nontrivial product in $\pi_*(S)$ by Adams-Novikov spectral sequence, where $\zeta_n$ is created by R. Cohen [1], $\gamma_s$ is a third periodic homotopy elements.
Funding Statement
Project supported by the National Science Foundation of China (No.11871284 and No.11761072).All authors contributed equally to this work.
Citation
Xing Gu. Xiangjun Wang. Jianqiu Wu. "The composition of R. Cohen's elements and the third periodic elements in stable homotopy groups of spheres." Osaka J. Math. 58 (2) 367 - 382, April 2021.
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