Homological Algebra
On the p-modular cohomology algebra of a finite p-group and a theorem of Serre
Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 417-420.

We solve a problem posed by E. Yalçin on the cohomology length of a p-group P, by providing bounds for the group theoretical invariant s(P) when p>2. These bounds improve the known bounds on the cohomology length of p-groups for odd p.

On obtient une borne pour la longueur cohomologique d'un p-groupe fini, p>2, résolvant ainsi un problème posé par E. Yalçin.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.003
Thas, Koen 1

1 Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Ghent, Belgium
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Thas, Koen. On the p-modular cohomology algebra of a finite p-group and a theorem of Serre. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 417-420. doi : 10.1016/j.crma.2007.01.003. http://www.numdam.org/articles/10.1016/j.crma.2007.01.003/

[1] Eisfeld, J.; Storme, L.; Szönyi, T.; Sziklai, P. Covers and blocking sets of classical generalized quadrangles, Shanghai, 1999 (Discrete Math.), Volume 238 (2001), pp. 35-51

[2] Klein, A.; Metsch, K. New results on covers and partial spreads of polar spaces, Innov. Incidence Geom., Volume 1 (2005), pp. 19-34

[3] O. Kroll, A representation theoretical proof of a theorem of Serre, Århus preprint, May 1986

[4] Metsch, K. Small point sets that meet all generators of W(2n+1,p), Des. Codes Cryptogr., Volume 31 (2004), pp. 283-288

[5] Minh, P.A. Serre's theorem on the cohomology algebra of a p-group, Bull. London Math. Soc., Volume 30 (1998), pp. 518-520

[6] Okuyama, T.; Sasaki, H. Evens' norm maps and Serre's theorem on the cohomology algebra of a p-group, Arch. Math., Volume 54 (1990), pp. 331-339

[7] Serre, J.-P. Sur la dimension cohomologique des groupes profinis, Topology, Volume 3 (1965), pp. 413-420

[8] Serre, J.-P. Une relation dans la cohomologie des p-groupes, C. R. Acad. Sci. Paris, Volume 304 (1987), pp. 587-590

[9] Thas, J.A. Ovoids, spreads and m-systems of finite classical polar spaces, Sussex, 2001 (London Math. Soc. Lecture Note Series), Volume vol. 288, Cambridge University Press, Cambridge (2001), pp. 241-267

[10] Yalçin, E. Set covering and Serre's theorem on the cohomology algebra of a p-group, J. Algebra, Volume 245 (2001), pp. 50-67

[11] E. Yalçin, Private communication, December 2006/January 2007

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