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The description of invariants of surfaces with respect to the motion groupsis reduced to the description of invariants of parameterized surfaces withrespect to the motion groups. Existence of a commuting system of invariantpartial differential operators (derivatives) and a finite system of invariants,such that any invariant of the surface is a function of these invariants andtheir invariant derivatives, is shown. The offered method is applicable in moregeneral settings than the "Moving Frame Method" does in differential geometry.

On relation between rational and differential rational invariants of surfaces with respect to the motion groups