Abstract
The symmetry properties of an isotropic non-Heisenberg magnet with the values of the magnetic ion spin S = 1 or S = 3/2 are studied in this work. It is shown that the systems are invariant under the transformation group SO(3) or SU(2). The conditions under which magnets with spin S = 1 or S = 3/2 are invariant with respect to the transformation groups SU(2S + 1) are determined. The study of the dynamic properties of the magnets under consideration has shown that at SU(2S + 1) points the systems become two-level, similarly to systems with magnetic ion spin S = 1/2.
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