I would like to find an appropriate reference for the following statement:
Statement. Let $M$ be a compact Riemannian manifold with non-negative Ricci curvature. Then $\pi_1(M)$ is virtually abelian.
It seems to me that the statement should follow from the article of Cheeger and Gromoll "The spletting theorem for manifolds of non-negative Ricci curvature" http://intlpress.com/JDG/archive/1972/6-1-119.pdf but since it is not stated explicitly in the article I am not 100% sure.
So, what would be a reference?