Let $(G, n)$ be a pair such that $n$ is a natural number, $G$ is a finite group which is abelian if $n \geq 1$. It is well-known that $\pi\_n(K(G,n)) = G$ and $\pi\_i (K(G,n)) = 0$ if $i \neq n$.


Also it is known that these spaces $K(G,n)$ play a very important role for cohomology. For any abelian group $G$, and any CW-complex $X$, the set $[X, K(G,n)]$ of homotopy classes of maps from $X$ to $K(G,n)$ is in natural bijection with the $n^{\mathrm{th}}$ singular cohomology group $H^n(X; G)$ with coefficients in $G$.


But what is known about the cohomology of the $K(G,n)$ themselves? It is interesting in the light of the above. Here I mean the singular cohomology with integral coefficients. 



(Co)homology of the Eilenberg-MacLane spaces K(G,n)
Computing the integral cohomology of $K(\pi,n)$'s is feasible but a bit tricky. In fact the only reference I know is [exposé 11 of H. Cartan's seminar, year 7](http://archive.numdam.org/ARCHIVE/SHC/SHC_1954-1955__7_1/SHC_1954-1955__7_1_A11_0/SHC_1954-1955__7_1_A11_0.pdf). I'd be interested if there are other sources that cover that.


