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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?

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    $\begingroup$ Is it not precisely Theorem 3 (pag 126) in the paper by Cheeger and Gromoll? $\endgroup$
    – Francesco Polizzi
    Commented Oct 24, 2012 at 12:11
  • $\begingroup$ Francesco, huge thanks! Of course you are right, I overlooked this theorem (shame for me :) ... ). $\endgroup$
    – aglearner
    Commented Oct 24, 2012 at 12:27

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The following paper has more than you want.

Wilking, Burkhard On fundamental groups of manifolds of nonnegative curvature. Differential Geom. Appl. 13 (2000), no. 2, 129–165.

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