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A family of nonzero products in the cohomology of the odd primary Steenrod algebra

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Abstract

Let \(p\) be a prime number greater than five and let \(A\) be the mod \(p\) Steenrod algebra. In this paper, we prove that the product \(h_n g_0 \tilde{\delta }_{s + 4}\in \mathrm{Ext}_A^{s+7,*}(\mathbb {F}_p,\mathbb {F}_p)\) is nontrivial, where \(n\geqslant 5\), \(0 \leqslant s < p - 4\). As a corollary, we obtain that the products \(h_ng_0\), \(h_n\tilde{\delta }_{s+4}\) and \(g_0\tilde{\delta }_{s+4}\) are all nontrivial.

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Authors and Affiliations

  1. School of Mathematical Sciences, Nankai University, Tianjin, 300071, People’s Republic of China

    Xiang Li

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Xiugui Liu

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  1. Xiang Li
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  2. Xiugui Liu
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Correspondence to Xiugui Liu.

Additional information

Research was partially supported by the NSFC (No. 11171161) and SRF for ROCS, SEM.

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Li, X., Liu, X. A family of nonzero products in the cohomology of the odd primary Steenrod algebra. Bol. Soc. Mat. Mex. 21, 89–97 (2015). https://doi.org/10.1007/s40590-014-0012-z

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  • DOI: https://doi.org/10.1007/s40590-014-0012-z

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