Abelian subgroups based on neutrosophic sets

Aiyared; C.; P. Maragatha; N.

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

Full Length Article

Volume 24 • Issue 2 • PP: 176-186 • 2024

Abelian subgroups based on neutrosophic sets

Aiyared Iampan ^1*

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,

C. Sivakumar ²

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,

P. Maragatha Meenakshi ²

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,

N. Rajesh ³

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¹Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand

²Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India

³Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.240215

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

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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.

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Iampan, Aiyared, Sivakumar, C., Meenakshi, P. Maragatha, Rajesh, N.. "Abelian subgroups based on neutrosophic sets." International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 2, 2024, pp. 176-186. DOI: https://doi.org/10.54216/IJNS.240215

Iampan, A., Sivakumar, C., Meenakshi, P., Rajesh, N. (2024). Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science, Volume 24(Issue 2), 176-186. DOI: https://doi.org/10.54216/IJNS.240215

Iampan, Aiyared, Sivakumar, C., Meenakshi, P. Maragatha, Rajesh, N.. "Abelian subgroups based on neutrosophic sets." International Journal of Neutrosophic Science Volume 24, no. Issue 2 (2024): 176-186. DOI: https://doi.org/10.54216/IJNS.240215

Iampan, A., Sivakumar, C., Meenakshi, P., Rajesh, N. (2024) 'Abelian subgroups based on neutrosophic sets', International Journal of Neutrosophic Science, Volume 24(Issue 2), pp. 176-186. DOI: https://doi.org/10.54216/IJNS.240215

Iampan A, Sivakumar C, Meenakshi P, Rajesh N. Abelian subgroups based on neutrosophic sets. International Journal of Neutrosophic Science. 2024;Volume 24(Issue 2):176-186. DOI: https://doi.org/10.54216/IJNS.240215

A. Iampan, C. Sivakumar, P. Meenakshi, N. Rajesh, "Abelian subgroups based on neutrosophic sets," International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 2, pp. 176-186, 2024. DOI: https://doi.org/10.54216/IJNS.240215

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