All Questions

Let $$1 \longrightarrow K \longrightarrow G \longrightarrow Q \longrightarrow 1$$ be a short exact sequence of groups and let $M$ be a $\mathbb{Z}[G]$-module. The Hochschild--Serre spectral ...

I probably don't understand something very basic about Hochschild-Serre spectral sequence. Let $G$ be a group with normal subgroup $N$ and $M$ a $G$-module with trivial action. Then as far as I ...

I am working in a problem group cohomology and nailed it down to compute a cohomology using an spectral sequence argument. The situation is as follows: Let $G = C_4 = \langle \sigma \rangle$ be the ...

For the symmetric group $S_3$, there is an inclusion $i:\mathbb{Z}/3\mathbb{Z}\hookrightarrow S_3$. How can I assert that the induced homomorphism $$i^{\ast}:H^{n}(S_3,\mathbb{Z})\rightarrow H^{n}(\...

Someone recently asks a question $SO(3)$ 2-cocycle trivialized to a 2-coboundary in $SU(2)$? now inspires me to revisit an earlier general question to ask an example of 3-cocycle $\omega_3^G$ of a ...