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High order perturbation theory corrections to the superfluid transitiontemperature in a weakly interacting Fermi gas with repulsive interaction arecalculated. This involves calculating the contributions of third and fourthorder diagrams in the gas parameter and taking into account effects ofretardation. The contributions from both second, third and fourth orders resultin the effective attraction in p-wave channel. It is shown that the criticaltemperature is mainly determined by second and third orders terms ofperturbation theory. The dependence of the critical temperature on an externalmagnetic field is found. We discuss possible applications of the results to thediluted 3He-4He mixtures and trapped neutral-atom Fermi gases.Comment: The version of the paper (JETP 90 (2000) 861) with author proofs,  which were not taken into account in translated journal publication. 21  pages, 12 figure

Superfluid transition temperature in a Fermi gas with repulsion allowing for higher orders of perturbation theory