  The exact solution of the Dirac equation and the spectrum of electron
quasi-energies in a superposition of the field of a circularly polarized
electromagnetic wave and a homogeneous magnetic field parallel to the direction
of wave propagation, are found taking into account the anomalous magnetic
moment. It is found that taking account of the anomalous magnetic moment
removes the spin degeneracy and that for intense fields the levels change
radically. The shift of the radiation frequency due to the intensity of the
wave field is found. This shift can be considerable.
