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The Lie symmetries of a large class of generalized Toda field theories arestudied and used to perform symmetry reduction. Reductions lead to generalizedToda lattices on one hand, to periodic systems on the other. Boundaryconditions are introduced to reduce theories on an infinite lattice to those onsemi-infinite, or finite ones.Comment: 26 pages, no figure

Point symmetries of generalized Toda field theories: II. Symmetry reduction