EuDML | Browse

Let $p \neq 2$ be a prime and let $G$ be a $p$ -group of matrices in ${SL}_{n} (ℤ)$ , for some integer $n$ . In this paper we show that, when $n < 3 (p - 1)$ , a certain subgroup of the cohomology group $H^{1} (G, 𝔽_{p}^{n})$ is trivial. We also show that this statement can be false when $n \geq 3 (p - 1)$ . Together with a result of Dvornicich and Zannier (see [2]), we obtain that any algebraic torus of dimension $n < 3 (p - 1)$ enjoys a local-global principle on divisibility by $p$ .

Cohomology of modules in the principal block of a finite group.

Benson, D.J. (1995)

The New York Journal of Mathematics [electronic only]

Cohomology of unipotent algebraic and finite groups and the Steenrod algebra.

Michishige Tezuka (1994)

Mathematische Zeitschrift

Cohomology rings of Artin groups

Claudia Landi (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper integer cohomology rings of Artin groups associated with exceptional groups are determined. Computations have been carried out by using an effective method for calculation of cup product in cellular cohomology which we introduce here. Actually, our method works in general for any finite regular complex with identifications, the regular complex being geometrically realized by a compact orientable manifold, possibly with boundary.

Compactly supported cohomology of systolic 3-pseudomanifolds

Roger Gómez-Ortells (2014)

Colloquium Mathematicae

We show that the second group of cohomology with compact supports is nontrivial for three-dimensional systolic pseudomanifolds. It follows that groups acting geometrically on such spaces are not Poincaré duality groups.

Complexity and Multiple Complexes.

David J. Benson, Jon F. Carlson (1987)

Mathematische Zeitschrift

Computing second cohomology of finite groups with trivial coefficients.

Ellis, Graham, Kholodna, Irina (1999)

Homology, Homotopy and Applications

Currently displaying 1 – 20 of 22

Page 1 Next