  Possible phase transitions between incompressible quantum Hall states and
compressible three-dimensional states are discussed for infinite-layer electron
systems in strong magnetic field. By variational Monte Carlo calculation,
relative stability of some trial states is studied. If the inter-layer distance
is large enough, the Laughlin state is stabilized for the Landau-level filling
\nu=1/3 of each layer. When the inter-layer distance is comparable to the
magnetic length, the Laughlin state becomes unstable against a different
fractional quantum Hall state with inter-layer correlation, and/or against a
three-dimensional compressible state. It is discussed how the quantum phase
transition between them can be controlled in actual systems.

Mesoscale and Nanoscale Physics