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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 Lie groups made discrete.

Pere Pascual Gainza (1990)

Publicacions Matemàtiques

We give a survey of the work of Milnor, Friedlander, Mislin, Suslin and other authors on the Friedlander-Milnor conjecture on the homology of Lie groups made discrete and its relation to the algebraic K-theory of fields.

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.

Cohomology with free coefficients of the fundamental group of a graph of groups.

Kenneth S. Brown, Ross Geoghegan (1985)

Commentarii mathematici Helvetici

Combinatorial squashings, 3-manifolds, and the third homology of groups.

A.J. Sieradski (1986)

Inventiones mathematicae

Commutative diagrams for the inflation-restriction sequence

Najar, Rudolph M. (1979)

Portugaliae mathematica

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

Congruences between Siegel modular forms on the level of group cohomology

Karsten Buecker (1996)

Annales de l'institut Fourier

Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of $G S p (4)$ , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...

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