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Characterization of the normal subgroups of finite index for the group representation of a Cayley tree

https://doi.org/10.17586/2220-8054-2016-7-5-888-892

Аннотация

 In this paper we give a characterization of normal subgroups for the group representation of the Cayley tree.

Ключевые слова


Об авторе

F. Haydarov
National University of Uzbekistan
Узбекистан


Список литературы

1. U.A. Rozikov. Gibbs measures on a Cayley trees, World Sci. Pub, Singapore, 2013.

2. Cohen D.E., Lyndon R.C. Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc., 1963, 108, P. 526–537.

3. Ganikhodjaev N.N., Rozikov U.A. Description of periodic extreme Gibbs measures of some lattice model on the Cayley tree, Theor. Math. Phys., 1997, 111, P. 480–486.

4. G.I. Botirov. Functional equations for the Potts model with competing interactions on a Cayley tree. Nanosystems: physics, chemistry, mathematics, 2016, 7(3), P. 401–404.

5. Young J.W. On the partitions of a group and the resulting classification, Bull. Amer. Math. Soc., 1927, 33, P. 453–461.

6. U.A. Rozikov, F.H. Haydarov. Normal subgroups of finite index for the group represantation of the Cayley tree, TWMS Jour. Pure. Appl. Math., 2014, 5, P. 234–240.

7. Kurosh A.G. Group theory, Akademic Verlag, Berlin, 1953.

8. D.S. Malik, J.N. Mordeson, M.K. Sen. Fundamentals of Abstract Algebra, McGraw-Hill Com., 1997


Рецензия

Для цитирования:


  . Наносистемы: физика, химия, математика. 2016;7(5):888-892. https://doi.org/10.17586/2220-8054-2016-7-5-888-892

For citation:


Haydarov F.H. Characterization of the normal subgroups of finite index for the group representation of a Cayley tree. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):888-892. https://doi.org/10.17586/2220-8054-2016-7-5-888-892

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)