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In this paper, we generalize the finite generation result of Sormani tonon-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces)with full support measures. This is a special case of the Milnor's Conjecturefor complete non-compact $RCD(0,N)$ spaces. One of the key tools we use is theAbresch-Gromoll type excess estimates for non-smooth spaces obtained byGigli-Mosconii.

Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth Have Finitely Generated Fundamental Groups