najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-888-892najo-1002Research ArticleСтатьиCharacterization of the normal subgroups of finite index for the group representation of a Cayley treeHaydarovF. H.
Tashkent
haydarov_imc@mail.ruNational University of UzbekistanUzbekistan20161508202575888892Copyright © Haydarov F.H., 20252025Haydarov F.H.Haydarov F.H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1002
In this paper we give a characterization of normal subgroups for the group representation of the Cayley tree.
Cayley treeGk-groupnormal subgrouphomomorphismepimorphismI am deeply grateful to Professor U.A. Rozikov for the attention to my work.I am deeply grateful to Professor U.A. Rozikov for the attention to my work.ReferencesU.A. Rozikov. Gibbs measures on a Cayley trees, World Sci. Pub, Singapore, 2013.U.A. Rozikov. Gibbs measures on a Cayley trees, World Sci. Pub, Singapore, 2013.Cohen D.E., Lyndon R.C. Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc., 1963, 108, P. 526–537.Cohen D.E., Lyndon R.C. Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc., 1963, 108, P. 526–537.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.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.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.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.Young J.W. On the partitions of a group and the resulting classification, Bull. Amer. Math. Soc., 1927, 33, P. 453–461.Young J.W. On the partitions of a group and the resulting classification, Bull. Amer. Math. Soc., 1927, 33, P. 453–461.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.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.Kurosh A.G. Group theory, Akademic Verlag, Berlin, 1953.Kurosh A.G. Group theory, Akademic Verlag, Berlin, 1953.D.S. Malik, J.N. Mordeson, M.K. Sen. Fundamentals of Abstract Algebra, McGraw-Hill Com., 1997D.S. Malik, J.N. Mordeson, M.K. Sen. Fundamentals of Abstract Algebra, McGraw-Hill Com., 1997
The authors declare that there are no conflicts of interest present.