I am trying to do an exercise in Brown's Cohomology of groups, but i have a few question of notation i guess
So its exercise $1.a)$, when he says the each $C_i$ is acyclic he means even for $0$? Also when he writes $H_*(C_G)$ does he mean the "normal" Homology of the complex i get when i change all the $C_i$ to $C_{iG}$? Thanks in advance.
New edit :
So far i was able to show that $H_n(G,M)\cong Ker\{(Ker \partial_{n-1})_G \rightarrow (C_{n-1})_G\}$, for $n >0$,is this correct?
He means that $C_0$, $C_1$, $C_2$ etc. are all $H_*$-acyclic.
By $H_*(C_G)$ he means the homology of the complex $$\cdots\to (C_2)_G \to (C_1)_G \to (C_0)_G\to0\to0\to\cdots$$ (and similarly in 1(b)).