I'm a student of mathematics and I need know about the status of the Milnor conjecture (if there are partial results or if someone solved that). The statement is:



> 
> A complete Riemannian manifold with non-negative Ricci curvature has a finitely generated fundamental group.
> 
> 
> 


If someone can help me with references to papers or anything I would be grateful.



Information about Milnor conjecture
According to David Roberts comment and the following paper it is open for dimensions $n\geq 4$.


*Pan, Jiayin*, [**A proof of Milnor conjecture in dimension 3**](http://dx.doi.org/10.1515/crelle-2017-0057), J. Reine Angew. Math. 758, 253-260 (2020). [ZBL1432.53053](https://zbmath.org/?q=an:1432.53053).


There is a nice survey by Shen and Sormani that can be found in author homepage:


*Shen, Zhongmin; Sormani, Christina*, [**The topology of open manifolds with nonnegative Ricci curvature**](http://www.arxiv.org/abs/math/0606774), Commun. Math. Anal., Conference 1, 20-34 (2008). [ZBL1167.53309](https://zbmath.org/?q=an:1167.53309).


And a few related and partial attacks to the conjecture:


*Paeng, Seong-Hun*, [**On the fundamental group of manifolds with almost nonnegative Ricci curvature**](http://dx.doi.org/10.1090/S0002-9939-03-06885-0), Proc. Am. Math. Soc. 131, No. 8, 2577-2583 (2003). [ZBL1040.53042](https://zbmath.org/?q=an:1040.53042).


*Xu, Senlin; Deng, Qintao*, The fundamental group of open manifolds with nonnegative Ricci curvature, Acta Math. Sin., Chin. Ser. 49, No. 2, 353-356 (2006). [ZBL1120.53021](https://zbmath.org/?q=an:1120.53021).


Which is stronger than


*Sormani, Christina*, [**Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups.**](http://dx.doi.org/10.4310/jdg/1214339792), J. Differ. Geom. 54, No. 3, 547-559 (2000). [ZBL1035.53045](https://zbmath.org/?q=an:1035.53045).


