  We study the many-body effects in a two-subband quasi-two-dimensional
electron system in a quantizing magnetic field at filling factor three. A
manifestation of these effects in the phonon absorption spectroscopy is
discussed. The electron system is mapped onto a two-level system with the
separation between levels determined by the intersubband splitting and the
cyclotron energy. The electron-electron interaction enhances the excitation
gap, which exists at all values of the interlevel splitting. This results in a
single-peak structure of the phonon absorption rate as a function of magnetic
field, instead of the double-peak structure for non-interacting electrons.
