The quantum Hall effect in a single-mode wire is studied for the first time
. It is established that a well-expressed quantum Hall resistance for filli
ng factors i=1 and 2 is observed in magnetic fields in which the magnetic l
ength becomes less than the width of the wire. Breakdown of proportionality
with respect to the magnetic field in the arrangement of the Hall quantiza
tion plateau and the dissipative conductivity minima is observed. (C) 1999
American Institute of Physics. [S1063-7826(99)01811-6].