  We study the effect that the electron-electron interaction has on the
properties of a multilayer electron system. We consider the case corresponding
to filling factor unity in each layer. We find that as a function of the sample
parameters the system has ferromagnetic, canted antiferromagnetic or
paramagnetic interlayer spin correlations. These three ground states are QHE
phases, because of the existence of a finite activation energy. In the
ferromagnetic phase the gap is due to the intrawell exchange energy, whereas in
the paramagnetic phase the gap appears due to the spatial modulation of the
interwell coherence.
