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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The essential ideal is a Cohen-Macaulay module


Author: David J. Green
Journal: Proc. Amer. Math. Soc. 133 (2005), 3191-3197
MSC (2000): Primary 20J06; Secondary 13C14
Published electronically: May 9, 2005
MathSciNet review: 2160180
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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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Additional Information

David J. Green
Affiliation: Department of Mathematics, University of Wuppertal, D-42097 Wuppertal, Germany
Email: green@math.uni-wuppertal.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07887-1
PII: S 0002-9939(05)07887-1
Received by editor(s): February 27, 2004
Received by editor(s) in revised form: June 24, 2004
Published electronically: May 9, 2005
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.