  In this note we discuss the fundamental groups and diameters of positively
Ricci curved $n$-manifolds. We use a method combining the results about
equivarient Hausdorff convergence developed by Fukaya and Yamaguchi with the
Ricci version of splitting theorem by Cheeger and Colding to give new
information on the topology of compact manifolds with positive Ricci curvature.
Moreover, we also obtain a weak Margulis's lemma for manifolds under a lower
Ricci curvature bound.
