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In order to constrain the initial mass function (IMF) of the first generation of stars (Population III), we investigate the fragmentation properties of metal-free gas in the context of a hierarchical model of structure formation. We investigate the evolution of an isolated 3-sigma peak of mass 2x10^6 M_solar which collapses at z_coll=30 using Smoothed Particle Hydrodynamics. We find that the gas dissipatively settles into a rotationally supported disk which has a very filamentary morphology.doi:10.1086/312385 pmid:10566986 fatcat:g7ez2beggnb2jogcde7dqa76am