Let $G$ be a $p$-adic Lie group, $H$ a subgroup of $G$. What is $H_1(H,\Lambda(G))$, where $\Lambda(G)$ is the Iwasawa algebra of $G$ over $\mathbb Z_p$?

If it simplies the question, we may assume $G$ is commutative. Or maybe even just $\mathbb Z_p^d$. I don't know how to do it even for this simple case.

I just realize that I have very few tools to compute group homology, unlike its cohomology cousins. A very embarrassing question: how do you compute group homology in general?



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