In this work we study the properties of a two-subband quasi-two-dimensional
electron system in a strong magnetic field when the electron filling factor is
equal to four. When the cyclotron energy is close to the intersubband splitting
the system can be mapped onto a four-level electron system with an effective
filling factor of two. The ground state is either a ferromagnetic state or a
spin-singlet state, depending on the values of the inter-level splitting and
Zeeman energy. The boundaries between these phases are strongly influenced by
the inter-electron interaction. A significant exchange-mediated enhancement of
the excitation gap results in the suppression of the electron-phonon
interaction. The rate of absorption of non-equilibrium phonons is calculated as
a function of Zeeman energy and inter-subband splitting. The phonon absorption
rate has two peaks as a function of intersubband splitting and has a step-like
structure as a function of Zeeman energy