  Results on the finite nonperiodic Toda lattice are extended to some
generalizations of the system: The relativistic Toda lattice, the generalized
Toda lattice associated with simple Lie groups and the full Kostant-Toda
lattice. The areas investigated, include master symmetries, recursion
operators, higher Poisson brackets, invariants, and group symmetries for the
systems. A survey of previous work on the classical Toda lattice is also
included.
