$H_{n-1}(M;\mathbb{Z})$ is a free abelian group need help with this problem:
show that if $M$ is closed connected oriented n-manifold then $H_{n-1}(M;\mathbb{Z})$ is a free abelian group.
thanx. 

By the universal coefficient theorem applied in degree $n$ to $H_n(X, R) \cong R$, any $\mathbb{Z}$-tor of $H_{n-1}(X, \mathbb{Z})$ vanishes, hence it is a flat, equivalently projective, equivalently free, $\mathbb{Z}$-module.
