The essential ideal is a Cohen-Macaulay module

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.

6 pages

References in corpus (2)

• The cohomology rings of rank 3 simple groups are Cohen-Macaulay
• On Carlson's depth conjecture in group cohomology

Cited by in corpus (2)

• Essential cohomology for elementary abelian p-groups
• Essential Cohomology of the p-Groups with a Cyclic Subgroup of Index p