If primordial fluctuations were isothermal their amplitude at recombination would be non-linear on scales Mo ≃ 106÷9 M⊙. Since the Jeans mass after recombination is MJo ≃ 8 × 105 Ω−1/2 M⊙ the clouds of mass Mo would be able to form the first generation of compact objects, the so-called Population III. These clouds would acquire angular momentum via tidal interactions with their neighbours. The importance of rotation can be conveniently characterised by the spin parameter λ = Vrotation/Vfree-fall and tidal interactions lead to a spin λo = 0.07 ± 0.03. As the cloud collapses λ increases as r−1/2. Any fragment forming in a rotating cloud would have the same spin λ as the whole cloud. It could therefore collapse only by ≃ λo 2 in radius before centrifugal forces intervened, thus leaving a large geometrical cross-section for coalescence to be important. At radii r ≲ λo 8/5 (Mo/MJo)2/15 ro the coalescence time is shorter than the free-fall time and no fragmentation is possible below this radius. In the primordial clouds two major factors prevent fragmentation at larger radii. First, the background radiation is still ‘hot’ and the trapping of it would prevent fragmentation until the whole cloud has collapsed to a radius 10−2 x−2/3 ro. Here x = 10−2(M/107 M⊙)1/3 is the ionization fraction given by the balance between gravitational contraction and recombination cooling. Furthermore, any small density fluctuation would lead to fragmentation only after the paternal cloud had collapsed by a factor (δ/5)2/3 in radius. For these reasons fragmentation is unlikely until centrifugal forces halt the collapse and a disk forms. The disk will be initially at T ≃ 104K but after a small fraction of H2 forms it will cool to T3 ≃ T/103K ≃ 1 and the final fragments mass could be as low as ≃ 0.2(λo/0.07)4 T3 2(MJo/Mo)1/3 M⊙.