  Relaxation of collective plasmon inter-Landau-level excitation is determined
by emission of LO-phonons or by Auger-like processes when this emission is
suppressed off the magneto-phonon resonance conditions. The decay of
"one-cyclotron" magneto-plasmons with wave-vectors near the roton minimum is
studied under the condition of filling $\nu=1$. Some features of this
relaxation should be helpful for the experimental detection of the
magneto-rotons in a strongly correlated 2D electron gas.
