Full use of symmetry in maximum-determinant rule

The properties of Hilbert space and group theory are used to point out the fact that the m-dimensional Laplace-Gauss law for m unknown structure factors, involving two Karle-Hauptman determinants, Δ_{m+ 1} and D_m, can take into account full symmetry information for any space group. It is shown that the ratio (Δ_{m+ 1}/D_m) is equal to a sum of ratios of Goedkoop determinants.