$\Tor^{\ZZ}_*(\ZZ/n, A)$

Let \(n\geq 1\), let \(C_n\coloneqq\ZZ/n\), let \(A\) be an abelian group, and let \(A[n]\coloneqq\ts{a\in A \st na = 0}\). The groups $\Tor^{\ZZ}_k(C_n, A)$ are \[ \Tor^{\ZZ}_0(C_n, A)\cong C_n\otimes_{\ZZ}A\cong A/nA,\qquad \Tor^{\ZZ}_1(C_n, A)\cong A[n],\qquad \Tor^{\ZZ}_k(C_n, A) = 0\quad (k\geq 2) \] [@Hat02].