Group Theory
Profinite groups of finite cohomological dimension
Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 353-358.

Let 1→NGG/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cdp(G)<∞ and if the order of ${H}^{k}\left(\mathrm{N},{𝔽}_{p}\right)$ is finite for k:=cdp(N), the virtual cohomological p-dimension of G/N equals nk.

Soit 1→NGG/N→1 une suite exacte courte de groupes profinis, et soit p un nombre premier. Nous montrons que si G a p-dimension cohomologique finie n:=cdp(G) et si l'ordre du groupe ${H}^{k}\left(\mathrm{N},{𝔽}_{p}\right)$ est fini pour k:=cdp(N), la p-dimension cohomologique virtuelle de G/N est égale à nk.

Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.022

Thomas Weigel 1; Pavel Zalesskii 2

1 Università degli studi di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8, 20126 Milano, Italy
2 Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil
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Thomas Weigel; Pavel Zalesskii. Profinite groups of finite cohomological dimension. Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 353-358. doi : 10.1016/j.crma.2003.12.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.022/

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