  We study the fundamental group of an open $n$-manifold $M$ of nonnegative
Ricci curvature. We show that if there is an integer $k$ such that any tangent
cone at infinity of the Riemannian universal cover of $M$ is a metric cone,
whose maximal Euclidean factor has dimension $k$, then $\pi_1(M)$ is finitely
generated. In particular, this confirms the Milnor conjecture for a manifold
whose universal cover has Euclidean volume growth and the unique tangent cone
at infinity.
