  The hidden symmetry of certain nano-magnets leads to many of the levels being
doubly degenerate for periodic values of the Zeeman energy. Corresponding to
such a symmetry is an operator, $K_{n}$, related to the time reversal operator,
and which commutes with the Hamiltonian. The degeneracies for whole integer
spin values are often similar to the Kramer's degeneracy for half-integer spin.
An all algebraic method for constructing Hamiltonians with such hidden
symmetries and different crystal symmetries is described.
