The group-homology tag has no usage guidance.

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### Homology of solvable Lie groups made discrete

In what follows "homology" will mean group homology, i.e. $H_*(BG^\delta;{\mathbf R})$ for the group $G$ with the discrete topology.
It is well-known how to compute the homology of abelian groups, ...

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### Is the Tensor/Exterior square $G\otimes G$ or $G\wedge G$ of infinite p-group also a p-group?

Let $G$ be an infinite countable p-group. Is it true that $G\otimes G$ or $G\wedge G$ are also p-groups? (where G acts on itself by conjugation). For simplicity, you can consider that $G=[G,G]$, and ...

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### Methods for showing homology of a subgroup survives to the larger group

Suppose we have an inclusion of groups $G_1<G_2$. I am curious about what methods there are out there for analyzing the map $H_k(G_1;\mathbb Q)\to H_k(G_2;\mathbb Q)$. In particular, what are tools ...

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### Cup-products and Transgression maps.

This question is related to Lyndon-Hochschild-Serre spectral sequence and cup products.
I have the followin result by J.S Milne in his book Arithmetic duality theorems pg 105.
Let $$0 \rightarrow C ...

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### Explicit transgression maps for Group homology in LHS

This question is related to another question of mine (Here: Lyndon-Hochschild-Serre spectral sequence and cup products).
I'm trying to figure out if some diagram commutes an one of the maps involved ...

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### Transgression maps in group cohomology and group homology / duality of spectral sequences

I am interested in whether the transgression maps for group cohomology and group homology are related via a version of the universal coefficient theorem.
Let $G$ be a group, $H$ a normal subgroup of ...