Abstract
Let p be an odd prime greater than seven and A the mod p Steenrod algebra. In this paper we prove that in the cohomology of A the product $h_1 h_n \tilde \delta _{s + 4}\in {\rm Ext}_A^{s + 6, t(s,n) + s} ({\bf Z}_p , {\bf Z}_p)$ is nontrivial for $n \geq 5$, and trivial for $n=3, 4$, where $ \tilde \delta _{s + 4}$ is actually $\tilde \alpha _{s+4}^{(4)}$ described by X. Wang and Q. Zheng, $0 \leq s < p - 4$, $t(s,n) = 2(p-1)[(s + 1) + (s + 3)p + (s + 3)p^2 + (s + 4)p^3 + p^n ].$ We show our results by explicit combinatorial analysis of the (modified) May spectral sequence. The method of proof is very elementary.
Citation
Xiugui Liu. He Wang. "On the cohomology of the mod p Steenrod algebra." Proc. Japan Acad. Ser. A Math. Sci. 85 (9) 143 - 148, November 2009. https://doi.org/10.3792/pjaa.85.143
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