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The definition and the criterion of Mei symmetry of generalized Hamilton systems with additional terms is studied in this paper. A necessary and sufficient condition for Mei symmetry of systems to be Lie symmetry is given. The Hojman conserved quantity for the differential equation of motion of generalized Hamilton system with additional terms being Mei symmetry can be deduced indirectly by Lie symmetry. An example is given to show the application of this result.
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