Essential cohomology and extraspecial 𝑝-groups

Minh, Pham

doi:10.1090/S0002-9947-00-02689-1

Essential cohomology and extraspecial $p$-groups
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Trans. Amer. Math. Soc. 353 (2001), 1937-1957 Request permission

Abstract:

Let $p$ be an odd prime number and let $G$ be an extraspecial $p$-group. The purpose of the paper is to show that $G$ has no non-zero essential mod-$p$ cohomology (and in fact that $H^{*}(G,\mathbb {F}_{p})$ is Cohen-Macaulay) if and only if $|G|=27$ and $exp(G)=3$.

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