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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kessar, Radha and Linckelmann, Markus 2012. On the Hilbert series of Hochschild cohomology of block algebras. Journal of Algebra, Vol. 371, p. 457.

    Symonds, Peter 2011. On the Castelnuovo-Mumford regularity of rings of polynomial invariants. Annals of Mathematics, Vol. 174, Issue. 1, p. 499.

  • Proceedings of the Edinburgh Mathematical Society, Volume 51, Issue 2
  • June 2008, pp. 273-284


  • David J. Benson (a1)
  • DOI:
  • Published online: 01 July 2008

Let $K$ be a field of characteristic $p$ and let $G$ be a finite group of order divisible by $p$. The regularity conjecture states that the Castelnuovo–Mumford regularity of the cohomology ring $H^*(G,K)$ is always equal to 0. We prove that if the regularity conjecture holds for a finite group $H$, then it holds for the wreath product $H\wr\mathbb{Z}/p$. As a corollary, we prove the regularity conjecture for the symmetric groups $\varSigma_n$. The significance of this is that it is the first set of examples for which the regularity conjecture has been checked, where the difference between the Krull dimension and the depth of the cohomology ring is large. If this difference is at most 2, the regularity conjecture is already known to hold by previous work.

For more general wreath products, we have not managed to prove the regularity conjecture. Instead we prove a weaker statement: namely, that the dimensions of the cohomology groups are polynomial on residue classes (PORC) in the sense of Higman.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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