Journal of applied mathematics & informatics

  • 제41권6호
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  • Pages.1237-1256
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ON THE FIBERS OF THE TREE PRODUCTS OF GROUPS WITH AMALGAMATION SUBGROUPS

  • ABDALLAH AL-HUSBAN (Department of Mathematics, Faculty of Science and Technology, Irbid National University) ;
  • DOAA AL-SHAROA (Department of Applied Science, Ajloun College, Al-Balqa Applied University) ;
  • RANIA SAADEH (Department of Mathematics, Faculty of Science, Zarqa University) ;
  • AHMAD QAZZA (Department of Mathematics, Faculty of Science, Zarqa University) ;
  • R.M.S. MAHMOOD (Department of Mathematics, Faculty of Science and Technology, Irbid National University)
  • 투고 : 2022.09.21
  • 심사 : 2023.09.26
  • 발행 : 2023.11.30
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초록

The tree products of groups with amalgamation subgroups are generalizations of the free products of groups with amalgamation subgroup. The aim of this paper is to construct a tree called the standard tree where the tree products of groups with amalgamation subgroups act without inversions and then find the quotient of this action. Furthermore, we show that if the amalgamation subgroups are finite and the factor groups act on disjoint trees then there exists a tree called the fiber tree where the tree products of groups with amalgamation subgroups act without inversions and find the quotients of this action. If each factor is a tree products with amalgamation subgroups, we get a new fiber tree and the corresponding factors.

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과제정보

The authors express their gratitude to the dear referees, who wish to remain anonymous, and to the editors, for their helpful suggestions, all of which improved the final version of this paper.

참고문헌

  1. A. Al-Husban, D. Al-Sharoa, M. Al-Kaseasbeh, and R.M.S. Mahmood, Structures of fibers of groups actions on graphs, WSEAS Trans. Math. 7 (2022), 650-658.  https://doi.org/10.37394/23206.2022.21.76
  2. A. Al-Husban, M. Al-Qadri, R. Saadeh, A. Qazza, & H. Almomani, Multi-Fuzzy Rings, WSEAS Trans. Math. 21 (2022), 701-706.  https://doi.org/10.37394/23206.2022.21.82
  3. L. Hawawsheh, A. Qazza, A.R. Saadeh, A. Zraiqat, & I. Batiha, Lp-Mapping Properties of a Class of Spherical Integral Operators, Axioms 12 (2023), 802. 
  4. A. Hazaymeh, R. Saadeh, H. Hatamleh, M. Alomari, & A. Qazza, A Perturbed Milne's Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates, Axioms 12 (2023), 803. 
  5. A. Hazaymeh, A. Qazza, R. Hatamleh, M. Alomari, & R. Saadeh, On Further Refinements of Numerical Radius Inequalities, Axioms 12 (2023), 807. 
  6. T. Qawasmeh, A. Qazza, R. Hatamleh, M. Alomari, & R. Saadeh, Further Accurate Numerical Radius Inequalities, Axioms 12 (2023), 801. 
  7. W. Dicks and M.J. Dunwoody, Groups Acting on Graphs, Cambridge University Press, 1989. 
  8. A. Karrass and D. Solitar, The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227-255.  https://doi.org/10.1090/S0002-9947-1970-0260879-9
  9. M.I. Khanfar and R.M.S. Mahmud, A note on groups acting on connected graphs, J. Univ. Kuwait Sci. 16 (1989), 205-208. 
  10. R.M.S. Mahmood, On the converse of the theory of groups acting on trees with inversions, Mediterr. J. of Math. 1 (2009), 89-106. 
  11. R.M.S. Mahmud, Presentation of groups acting on trees with inversions, Proc. R. Soc. Edinb. Sect. A 113 (1989), 235-241.  https://doi.org/10.1017/S0308210500024100
  12. J.P. Serre, Trees, Translated by John Stillwell, Springer-Verlag, 1980.