The finite Hubbard lattice with strong repulsion away from half-filling in a strong magnetic field is considered. The exact ground state energies and density-density correlation function for electrons in the high-spin limit with one spin-flip state (Nagaoka instability) is calculated for an arbitrary number of electrons and lattice sites in periodic hypercubes in one, two and three dimensions. The criteria for stability of either the spin-flipped phase or saturated Nagaoka state at large U and finite doping are derived.
