  The ground states of electrons in two vertically coupled quantum dots in the
presence of an external magnetic field have been studied within the density
functional theory. A phase diagram of the transition to the quantum Hall state
in double quantum dots has been plotted for the Landau level filling factor
$\nu = 1$. It has been shown that the quantum Hall state can be stable for a
zero tunnel splitting. The influence of the impurity potential on the stability
condition for the quantum Hall state has been analyzed.
