  Recently we have computed the third order corrections to the ground state
energy of the arbitrarily polarized diluted gas of spin 1/2 fermions
interacting through a spin-independent repulsive two-body potential. Here we
extend this result to the gas of spin $s$ fermions - a system the Hamiltonian
of which has an accidental $SU(2s+1)$ symmetry - with arbitrary densities of
fermions having different spin projections. The corrections are computed
semi-analytically using the effective field theory approach and are
parametrized by the $s$- and $p$- wave scattering lengths $a_0$ and $a_1$ and
the $s$-wave effective radius $r_0$, measurable in the low energy
fermion-fermion elastic scattering. The result is used to study the impact the
higher order corrections can have on the characteristics of the phase
transition (at zero temperature) to the ordered phase (on the emergence of the
itinerant ferromagnetism).
