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Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings as Fe_6, Cu_6, Fe_{10}, some planar macromolecules as Fe_{12} or Fe_8) the symmetry group is isomorphic with the dihedral group D_N. In this paper group-theoretical "parameters" of such groups are determined, especially...
A finite spin system invariant under a symmetry group G is a very illustrative example of a finite group action on mappings f: X → Y (X is a set of spin carriers, Y contains spin projections for a given spin number s). Orbits and stabilizers are used as additional indices of the symmetry adapted basis. Their mathematical nature does not decrease a dimension of a given eigenproblem, but they label...
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