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Essential cohomology and extraspecial $p$-groups


Author: Pham Anh Minh
Journal: Trans. Amer. Math. Soc. 353 (2001), 1937-1957
MSC (2000): Primary 20J06; Secondary 20D15, 55R40
DOI: https://doi.org/10.1090/S0002-9947-00-02689-1
Published electronically: November 29, 2000
MathSciNet review: 1813600
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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 $\vert G\vert=27$ and $exp(G)=3$.


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Additional Information

Pham Anh Minh
Affiliation: Department of Mathematics, College of Sciences, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Address at time of publication: 53 Craig Road, Stockport SK4 2AP, England
Email: paminh@dng.vnn.vn, minhp@vol.vnn.vn

DOI: https://doi.org/10.1090/S0002-9947-00-02689-1
Received by editor(s): September 10, 1999
Published electronically: November 29, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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