RCD(0,N)-spaces with small linear diameter growth

In this paper, we study some structure properties on the (revised) fundamental group of RCD(0,N) spaces. Our main result generalizes earlier work of Sormani on Riemannian manifolds with nonnegative Ricci curvature and small linear diameter growth. We prove that the revised fundamental group is finitely generated if assuming small linear diameter growth on RCD(0,N) spaces.