# Tagged Questions

108 views

### Successive Schur covers

Let $G_0$ be a finite group and $G_j$ a Schur cover of $G_{j-1}$ for $j=1,2,3\ldots$. Is $G_2$ equal to $G_1$? If not, will the sequence stop after finite steps in general?
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### The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$

Let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible ...
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### Non split extension isomorphic (as a group) to a split extension

$\def\Z{\mathbb{Z}}$ Let $A$ be a finite abelian group and $G$ a finite group acting on $A$. Then the extension $0 \to A \to E \to G \to 1$ is splits if and only if the corresponding $2$-cocycle is ...
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### 3-cocycle representatives for the dihedral group $D_{2n}$?

I am looking for a reference for a complete list of 3-cocycle representatives for $H^3(D_{2n},\mathbb{C}^\times)$, where $$D_{2n}=\langle a, b\mid a^2=b^2=(ab)^n=e\rangle$$ is the dihedral group of ...
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### n-cocycles of finite abelian groups from cohomology group

Question: Given a generic finite abelian group $G=\mathbb{Z}_{N^{(1)}} \times \cdots \times \mathbb{Z}_{N^{(k)}}$. (1) What is the explicit forms of its cohomology group (see my definition) in a ...
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### Group cochains invariant under the action of the symmetric group

Let $G$ be a finite group and $A$ an abelian group. Recall the cochain groups $$C^k = \{f: G^k \to A\}$$ and the coboundary map $$\delta : C^k \to C^{k+1}$$  (\delta f)(g_1, \ldots, g_{k+1}) ...
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### Obstruction to extension of non-abelian groups - finite example?

Let $G$ be a non-abelian group, let $\Pi$ be a group, and let $\eta: \Pi\rightarrow Out(G)$ be a homomorphism, where $Out(G)$ is the group of automorphisms of G modulo the normal subgroup of inner ...
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### Crossed modules and degree-3 group cohomology

It is well known (see e.g. K. Brown, "Cohomology of groups") that a degree-3 cohomology class of a group G with coefficients in a module A can be thought of as an equivalence class of crossed modules, ...
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### Inseparable Galois Cohomology

First let me give a general form of my question, and then I'll give some motivation and a more specific version of it. Let $K/k$ be a Galois extension of fields with Galois group $G$, and let $X$ be ...
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### A question about finite groups.

Let $k$ be a positive integer. Is it true that any finite group $H$ of cardinal $4k+2$ whose center contains an element $h$ of order $2$ is isomorphic to the direct product ...