  The many-body theory of a uniform electron gas was developed at the end of
1950ies. The Coulomb interaction between electrons was considered as a
perturbation and the ground state energy was calculated in all orders of the
non-degenerate perturbation theory. We show that the ground state of the
unperturbed system is actually strongly degenerate and that the degenerate
perturbation theory leads to lower values of the ground state energy.
