Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 213–217 | Cite as

New Normal Subgroups for the Group Representation of the Cayley Tree

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Abstract

In this paper it is given a full description of normal subgroups of index eight and ten for the group representation of a Cayley tree and counted all of them.

Keywords and phrases

Gk-group normal subgroup homomorphism epimorphism 

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References

  1. 1.
    D. E. Cohen and R. C. Lyndon, “Free bases for normal subgroups of free groups,” Trans. Am.Math. Soc. 108, 526–537 (1963).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    D.S. Malik, J. N. Mordeson, and M.K. Sen, Fundamentals of Abstract Algebra (McGraw-Hill, New York, 1997).Google Scholar
  3. 3.
    N. N. Ganikhodjaev and U. A. Rozikov, “Description of periodic extreme Gibbs measures of some lattice model on the Cayley tree,” Theor. Math. Phys. 111, 480–486 (1997).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    U. A. Rozikov and F. H. Haydarov, “Normal subgroups of finite index for the group represantation of the Cayley tree,” TWMS J. Pure Appl.Math. 5, 234–240 (2014).MathSciNetMATHGoogle Scholar
  5. 5.
    U. A. Rozikov, GibbsMeasures on a Cayley Trees (World Scientific, Singapore, 2013).CrossRefGoogle Scholar
  6. 6.
    A. G. Kurosh, Group Theory (Akademic Verlag, Berlin, 1953).MATHGoogle Scholar
  7. 7.
    J.W. Young, “On the partitions of a group and the resulting classification,” Bull. Am.Math. Soc. 33, 453–461 (1927).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.National University of UzbekistanTashkentUzbekistan

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