  Let (M,d) be a metric space. For 0<r<R, and p in M let G(p,r,R) be the group
obtained by considering all loops based at p whose image is contained in the
closed ball of radius r and identifying two loops if there is a homotopy
betweeen them that is contained in the open ball of radius R. In this paper we
study the asymptotic behavior of the G(p,r,R) groups of complete open manifolds
of nonnegative Ricci curvature. We also find relationships between the G(p,r,R)
groups and tangent cones at infinity of a metric space and show that any
tangent cone at infinity of a complete open manifold of nonnegative Ricci
curvature and small linear diameter growth is its own universal cover.
