In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of ...

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### Cohomology of $\mathbb Z_4$ via the Lyndon-Hochschild-Serre spectral sequence

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### Kunneth formula for semidirect product

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### The third (co)homology group

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### Relationship between irreducible representations of the Schur covering group and elements of $H^2(G,U(1))$

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### Trivializing unitary cocycles in abelian von Neumann algebras that are uniformly close to the trivial one

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### Restricting projective representations of Lie groups to lattices

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### Minimal parabolic subgroups are $G(k)$-conjugate: a cohomological interpretation?

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### Trivial cohomology with free module coefficient

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### Monoid cohomology of $\mathbb{N}$ for a linear algebraic group

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### Description of Shapiro lemma by cochain

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### Finite group representation as $\mathrm{Aut}(\Gamma)$ action $H^1(\Gamma,\mathbb{Z})$ of graph?

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### When is a sequence of group extensions associative?

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### Small modules over finite group with large cohomology

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### Example of group cohomology not annihilated by exponent of $G$?

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### primary decomposition for nonabelian cohomology of finite groups

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### Interpreting $H^n(BG,\mathbb Z)$ when $G$ is an infinite discrete group

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### Calculation of the Schur multiplier of $\mathbb Z^2$

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### Contracting the rational bar cocomplex for a finite group G

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### Projective resolutions of finite-dimensional representations of infinite groups

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### How to show the equality of two descriptions for the cohomology of a non-finite group

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### Number of surjections of a given complexity

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### Isomorphism in homology

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### Is the cohomology ring of a finite group computable?

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### Computation of group homology $H_2 ((\mathbb{Z}/3\mathbb{Z}) \rtimes (\mathbb{Z}/4\mathbb{Z}),\mathbb{Z})$

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### Cohomology of root data

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### A cohomology associated to a Riemannian manifold

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### Homology of $\mathrm{PGL}_2(F)$

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### Pull back group cohomology onto handle decomposition

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### A functor on the category of commutative rings, algebras or Banach algebras

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### A possible generalization of “Group Cohomolgy”

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### Group (Co)Homology of Symmetric Group

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### Using Dunwoody's results on cohomological dimension to learn about a von Neumann regular group ring

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### How to compute the group cohomology of $\mathbb{Z}/n\mathbb{Z}\times \mathbb{Z}/n\mathbb{Z}$ with coefficient in a trivial module?

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### cohomology of finite groups of lie type with coefficients in the adjoint module

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### Use GAP program to obtain explicit cocycles in group cohomology

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### A finite group that splits and does not split

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### Equivalence of finiteness of $spliG$ and periodicity isomorphisms being induced by cup product

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### Kazhdan constant and finite index subgroups

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### Presentations of superperfect groups

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### A question about continuous group cohomology

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### A group of type F that is an extension of type F-by-type F

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### On an inequality concerning the strict cohomological dimension of a profinite group

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### Calculating cohomology group $H^3(point group,\mathbb{Z})$ using GAP program

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### Trivial Tate modules

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### Is there a composite-order generalization of the homomorphism on Rep(Z/p) giving total dimension of Tate cohomology?

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### Cohomology of Infinite Dimensional Lie Algebra

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### a universal module for group cohomology?

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### Lower bounds for the top rational cohomology of arithmetic groups

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### Computing an explicit homotopy inverse for $B(*,H,*) \hookrightarrow B(*,G,G/H)$

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