Essential cohomology and extraspecial $p$-groups.

Pham Anh Minh
Department of Mathematics
College of Sciences
University of Hue
Dai hoc Khoa hoc
Hue
Vietnam

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 (hence, $H^*(G,\mathbb F_p)$ is Cohen-Macaulay) if and only if
$|G| = 27$ and $exp(G) = 3$.