Geodesic
On normal subgroups of the group representation of the Cayley tree
Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 4, pp. 135-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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Gibbs measure plays an important role in statistical mechanics. On a Cayley tree, for describing periodic Gibbs measures for models in statistical mechanics we need subgroups of the group representation of the Cayley tree. A normal subgroup of the group representation of the Cayley tree keeps the invariance property which is a significant tool in finding Gibbs measures. By this occasion, a full description of normal subgroups of the group representation of the Cayley tree is a significant problem in Gibbs measure theory. For instance, in [1, 2] a full description of normal subgroups of indices four, six, eight, and ten for the group representation of a Cayley tree is given. The present paper is a generalization of these papers, i. e., in this paper, for any odd prime number $p$, we give a characterization of the normal subgroups of indices $2n$, $n\in\{p, 2p\}$ and $2^i, i\in \mathbb{N},$ of the group representation of the Cayley tree. 
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F. H. Haydarov. On normal subgroups of the group representation of the Cayley tree. Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 4, pp. 135-142. http://geodesic.mathdoc.fr/item/VMJ_2023_25_4_a11/

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