The magneto-luminescence of GaN/AlGaN quantum wells in fields up to 52T shows a field dependence that is strongly dependent on the well width. Strong redshifts are seen for the narrowest wells that are attributed to a Zeeman splitting. This is unexpected, since in bulk GaN epilayers the electron and hole g-factors of the lowest valence band cancel each other almost exactly. Therefore, we attribute this splitting to a reordering of the valence band due to the different band offsets caused by the strain and the aluminium component in the AlGaN barriers. The field dependence also gives information on the size of the exciton that has been converted into values for the exciton binding energy, and these values agree reasonably well with a theory that includes the presence of the electric field.