  We investigate the magnetoresistance of epitaxially grown, heavily doped
n-type GaAs layers with thickness (40-50 nm) larger than the electronic mean
free path (23 nm). The temperature dependence of the dissipative resistance
R_{xx} in the quantum Hall effect regime can be well described by a hopping law
(R_{xx} \propto exp{-(T_0/T)^p}) with p=0.6. We discuss this result in terms of
variable range hopping in a Coulomb gap together with a dependence of the
electron localization length on the energy in the gap. The value of the
exponent p>0.5 shows that electron-electron interactions have to be taken into
account in order to explain the occurrence of the quantum Hall effect in these
samples, which have a three-dimensional single electron density of states.
