  The results of recent measurements of the cyclotron resonance (CR) spectra
for a GaAs quantum well are interpreted in terms of the resonant magnetopolaron
effect. Owing to this effect, the CR peaks split near the TO-phonon frequency
and also change their positions with respect to those obtained without
electron-phonon interaction. The theoretical peak positions of the CR spectra
calculated within the many-polaron approach compare well with experimental
data, as distinct from the CR energies calculated without electron-phonon
interaction, which show no particular features in the region of the
optical-phonon frequencies. We conclude that the Froehlich polaron concept is
valid and even necessary to interpret the CR spectra of quantum wells.
