In 1968, Milnor conjectured that any complete noncompact manifold, M, with nonnegative Ricci curvature has a finitely generated fundamnetal group. In this paper, we prove there exists a universal contant, S, depending only on the dimension, such that the following theorems hold.
Theorem I: If M has small linear diameter growth, diam(r)<4Sr, then the manifold has a finitely generated fundamental group.
Theorem II: If M has an infinitely generated fundamental group, then it has a tangent cone at infinity, Y, which does not have a pole at its base point. In fact if Z is a length space such that the Gromov-Hausdorff distance from Z to Y is less than S/4, then the base point of Z is not a pole.
Corollary: Let M be a complete noncompact manifold with nonnegative Ricci curvature. If M has linear volume growth then it has a finitely generated fundamental group.
These theorems are proven using two main lemmas. The first creates a sequence cut points in M by choosing a special sequence of generators of the fundamental group. The second uniformly estimates how cut these points are using Abresch and Gromoll's Excess Theorem.