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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 2 , PP: 176-186, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Abelian subgroups based on neutrosophic sets

Aiyared Iampan 1 * , C. Sivakumar 2 , P. Maragatha Meenakshi 3 , N. Rajesh 4

  • 1 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand - (aiyared.ia@up.ac.th)
  • 2 Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India - (sivaias777@gmail.com)
  • 3 Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India - (maragathameenakship@gmail.com)
  • 4 Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India - (nrajesh topology@yahoo.co.in)

    • Doi: https://doi.org/10.54216/IJNS.240215

    Received: October 28, 2023 Revised: February 15, 2024 Accepted: April 22, 2024
    Abstract

    The notion of a neutrosophic Abelian subgroup of a group is introduced. The characterizations of a neutrosophic Abelian subgroup are investigated. We show that the homomorphic preimage of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup, and the onto homomorphic image of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup.

    Keywords :

    neutrosophic group , neutrosophic Abelian subgroup , neutrosophic cyclic subgroup.

    References

    [1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1), (1986), 87-96.

    [2] J. Gallian, Contemporary Abstract Algebra, 8th ed. Boston, MA, USA: Cengage Learning, 2012.

    [3] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (fourth edition), Rehoboth American Research Press, 2008.

    [4] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3), (2005), 287-297.

    [5] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353.

    Cite This Article As :
    Iampan, Aiyared. , Sivakumar, C.. , Maragatha, P.. , Rajesh, N.. Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 176-186. DOI: https://doi.org/10.54216/IJNS.240215
    Iampan, A. Sivakumar, C. Maragatha, P. Rajesh, N. (2024). Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science, (), 176-186. DOI: https://doi.org/10.54216/IJNS.240215
    Iampan, Aiyared. Sivakumar, C.. Maragatha, P.. Rajesh, N.. Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science , no. (2024): 176-186. DOI: https://doi.org/10.54216/IJNS.240215
    Iampan, A. , Sivakumar, C. , Maragatha, P. , Rajesh, N. (2024) . Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science , () , 176-186 . DOI: https://doi.org/10.54216/IJNS.240215
    Iampan A. , Sivakumar C. , Maragatha P. , Rajesh N. [2024]. Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science. (): 176-186. DOI: https://doi.org/10.54216/IJNS.240215
    Iampan, A. Sivakumar, C. Maragatha, P. Rajesh, N. "Abelian subgroups based on neutrosophic sets," International Journal of Neutrosophic Science, vol. , no. , pp. 176-186, 2024. DOI: https://doi.org/10.54216/IJNS.240215

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