  We investigate a finite two-dimensional system in the presence of external
magnetic field. We discuss how the energy spectrum depends on the system size,
boundary conditions and Coulomb repulsion. On one hand, using these results we
present the field dependence of the transport properties of a nanosystem. In
particular, we demonstrate that these properties depend on whether the system
consists of even or odd number of sites. On the other hand, on the basis of
exact results obtained for a finite system we investigate whether the
Hofstadter butterfly is robust against strong electronic correlations. We show
that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when
the magnetic field increases.
