The essential ideal is a Cohen–Macaulay module

Green, David

doi:10.1090/S0002-9939-05-07887-1

The essential ideal is a Cohen–Macaulay module
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by David J. Green PDF

Proc. Amer. Math. Soc. 133 (2005), 3191-3197 Request permission

Abstract:

Let $G$ be a finite $p$-group which does not contain a rank two elementary abelian $p$-group as a direct factor. Then the ideal of essential classes in the mod-$p$ cohomology ring of $G$ is a Cohen–Macaulay module whose Krull dimension is the $p$-rank of the centre of $G$. This basically answers in the affirmative a question posed by J. F. Carlson (Question 5.4 in Problems in the calculation of group cohomology, 1999).

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