  The induced intraspecies interactions among the majority species, mediated by
the minority species, is computed for a population-imbalanced two-component
Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is
dominant for equal populations, leading to singlet s-wave pairing, we find that
in the strongly imbalanced regime the induced intraspecies interaction leads to
p-wave pairing and superfluidity of the majority species. Thus, we predict that
the observed spin-polaron Fermi liquid state in this regime is unstable to
p-wave superfluidity, in accordance with the results of Kohn and Luttinger,
below a temperature that, near unitarity, we find to be within current
experimental capabilities. Possible experimental signatures of the p-wave state
using radio-frequency spectroscopy as well as density-density correlations
after free expansion are presented.
