We report here a study of a specific doublet of de Haas-van Alphen frequencies in pure Mg and very dilute Mg(Cd) alloys with the magnetic field aligned with the c-axis. The work involved three stages. First, the use of extremely strain-free crystals, temperatures down to 40 millidegree Kelvin, large amplitude modulation, and the fast Fourier transform allowed the components of this doublet to be well resolved. This resolution allowed measurement of the changes in the cross-sectional area as a function of magnetic field orientation to verify the assignment of this doublet to the cap and monster arm junction at the top of the Brillouin zone. Third, with the magnetic field aligned with the c-axis, the splitting of this doublet offered a direct and sensitive indication of any symmetry breaking changes in the 0001 Fourier component of the ionic lattice potential in Mg upon the introduction of Cd. C. B. Friedberg's analysis of his electron interference lineshape data from the quantum interferometer in Mg had indicated that the energy of this band gap should increase by 40% with the introduction of 15 ppm Cd. Our data indicate that any change in the energy of the band gap must be at least three orders of magnitude smaller than that indicated by Friedberg. Our data are, in fact, consistent with there being no changes in the electronic band structure or the Fermi surface of Mg(Cd) alloys (with up to 0.02% (At) Cd), from that of pure Mg.