  In this article, we prove that the fundamental group $\pi_1(M)$ of a complete
open manifold $M$ with nonnegative Ricci curvature is finitely generated, under
the condition that the Riemannian universal cover $\tilde M$ satisfies an
"almost $k$-polar at infinity" condition. Additionally, such $\pi_1(M)$ is
virtually abelian. Furthermore, we demonstrate that the base point of any
tangent cone at infinity of such a manifold is nearly a pole. In the case where
$\tilde M$ exhibits almost maximal Euclidean volume growth, we prove that $M$
deformation retracts to a closed submanifold $F$ which is diffeomorphic to a
flat manifold, provided $M$ is not simply connected.
