Partition structures of the cayley tree and applications for describing periodic gibbs distributions

In the group representation of the Cayley tree, the distribution of elements of the partition into conjugate classes of finite-index, normal subgroups is described. For the inhomogeneous Ising model, it is proved that there exist only three H₀-periodic Gibbs distributions, where H₀ is a normal subgroup of finite index. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 170–175.