THE NEUTROSOPHIC HOM - GROUPS AND NEUTROSOPHIC HOM - SUBGROUPS I
Keywords:
Hom-groups, Hom-subgroups, neutrosophicgroups, neutrosophic subgroups, neutrosophic hom groups, neutrosophic hom subgroups
Abstract
Hom-groups are the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. The neu-
trosophic set is a powerful tool in dealing with incomplete, indeterminate and inconsistent data that exist in the real world. Neutrosophic set is characterized
by the truth membership function in the set (T), indeterminacy membership function in the set (I) and falsity membership function in the set (F) where
0 ≤ T + I + F ≤ 3+. In this work, eorts are intensied to clearly exemplify and create distinctions between certain structural ( classical ) groups , which
are neutrosophic Hom groups and those which are not. Some examples of the neutrosophic Hom groups are also carefully constructed with elementary fea-
tures and characterizations such as the subgroup series as well as their lattices. Finally , the certainty of the Lagranges theorem involving the subgroup of any
nite neutrosophic Hom - group G(I)
References
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(DOI:10.5281/zenodo.3728222)
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[15] M. Hassanzadeh, Hom-groups, representations and homological algebra, Colloq. Math., 158, 2019 ,21-38.
[16] M.A. Ibrahim., A.A.A. Agboola., E.O. Adeleke., and S.A. Akinleye, Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup International Journal of Neutrosophic Science (IJNS), 2 (1), 2020 , 47-62. (DOI:10.5281/zenodo.3724603)
[17] I.M. Isaacs, Finite Group Theory, American Mathematical Society, Providence, RI., 2008
[18] J. Jiang,, S.K. Mishra., and Y. Sheng, Hom-Lie algebras and Hom-Lie groups, integration and differentiation. SIGMA Symmetry Integrability Geom. methods Appl., 16 (137), 2020, 22.
[19] C. Laurent-Gengouxa., A. Makhlouf., and J. Teles, Universal algebra of a Hom-Lie algebra and group-like elements, Journal of Pure and Applied Algebra, 222 (5), 2018 , 1139-1163.
[20] U.C. Liang., Q.F. Tian., M. Yao., and S. Ripan On Homgroups and Hm-group Actions, Acta Mathematica, English Series, 39, 2023 , 1887-1906. https://doi.org/10.1007/s10114-023-2133-7, http://www.ActaMath.com.
[21] F. Smarandache, Neutrosophy, Neutrosophic Probability,. Set, and Logic, ProQuest Information and Learning, Ann Arbor, Michigan, USA, 105 p. http://fs.unm.edu/eBook-Neutrosophic6.pdf (edition online), 1998
[22] F. Smarandache, (T,I,F)- Neutrosophic Structures, Neutrosophic Sets and Systems (NSS), 8, 2015, 3-10.
[23] F. Smarandache, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers. In Symbolic Neutrosophic Theory, Chapter 7, Europa Nova, Brussels, Belgium, 2015 ,186-193.
[24] W.B. Vasantha Kandasamy., and F. Smarandache, Neutrosophic Rings, Hexis, Phoenix, Arizona. http://fs.unm.edu/NeutrosophicRings.pdf, 2006
[25] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (2006) , 1965 , 338-353.
[26] A.A.A Agboola A.A.A , On Refined Neutrosophic Quotient Groups, International Journal of Neutrosophic Science (IJNS) Vol. 5, No. 2, 2020 , PP. 76-82
[27] M. Hassanzadeh, Lagranges theorem for Hom-groups, Rocky Mountain J. Math., 49, 2019, 773787
[28] Grigore Calugareanu , The total number of subgroups of a finite abelian, group Scientiae Mathematicae Japonicae online, vol. 10, 2003 ,207217
[29] M. Suzuki M, On the lattice of subgroups of nite groups. Trans. Amer. Math. Soc., 70, 1951 , 345-371.
[30] A.A.A. Agboola, Introduction to Neutrosophic Hom-group, J. Mahani Math. Res. ( To appear )
[2] A.A.A. Agboola, A.D. Akinola., and O.Y. Oyebola, Neutrosophic Rings I, Int. J. of Math. Comb., 4, 2011, 1-14.
[3] A.A.A. Agboola, E.O. Adeleke., and S.A. Akinleye, Neutrosophic Rings II, Int. J. of Math. Comb., 2, 2012, 1-8.
[4] A.A.A Agboola, On Re ned Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems (NSS), 10, 2015 99-101.
[5] A.A.A. Agboola., and B. Davvaz., On Neutrosophic Canonical Hypergroups and Neutrosophic Hyperrings, Neutrosophic Sets and Systems (NSS), 2, 2014, 34-41.
[6] A.A.A Agboola,, B. Davvaz., and F. Smarandache, Neutrosophic Quadruple Hyperstructures, Annals of Fuzzy Mathematics and Informatics, 14, 2017 ,29-42.
[7] T. Bera and N.K. Mahapatra, Study of the group theory in neutrosophic soft sense, Asia Mathematica, Vol. 3(2), pp. 1-18, 2019.
[8] E.O. Adeleke., A.A.A Agboola., and F. Smarandache, Refined Neutrosophic Rings I, International Journal of Neutrosophic Science (IJNS), 2 (2), 2020, 77-81.
(DOI:10.5281/zenodo.3728222)
[9] E.O. Adeleke, A.A.A Agboola., and F. Smarandache, Refined Neutrosophic Rings II, International Journal of Neutrosophic Science (IJNS), 2 (2), 2020 , 89-94.
(DOI:10.5281/zenodo.3728235)
[10] S.A. Akinleye., F. Smarandache ., and A.A.A. Agboola, On Neutrosophic Quadruple Algebraic Structures, Neutrosophic Sets and Systems (NSS), 12, 2016 , 122-126.
[11] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems (FSS), 20, 1986, 87-96.
[12] I. Gilbert and J. Gilbert, Elements of Modern Algebra, Eight Edition, Cengage Learning,
USA, 2015
[13] J.T. Hartwig., D. Larson., and S .D. Silvestrov, Deformations of Lie Algebras using - derivations, J. Algebra, 295, 2006, 314-361.
[14] M. Hassanzadeh, Lagranges theorem for Hom-groups, Rocky J.Math., 49, 2019 , 773- 787.
[15] M. Hassanzadeh, Hom-groups, representations and homological algebra, Colloq. Math., 158, 2019 ,21-38.
[16] M.A. Ibrahim., A.A.A. Agboola., E.O. Adeleke., and S.A. Akinleye, Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup International Journal of Neutrosophic Science (IJNS), 2 (1), 2020 , 47-62. (DOI:10.5281/zenodo.3724603)
[17] I.M. Isaacs, Finite Group Theory, American Mathematical Society, Providence, RI., 2008
[18] J. Jiang,, S.K. Mishra., and Y. Sheng, Hom-Lie algebras and Hom-Lie groups, integration and differentiation. SIGMA Symmetry Integrability Geom. methods Appl., 16 (137), 2020, 22.
[19] C. Laurent-Gengouxa., A. Makhlouf., and J. Teles, Universal algebra of a Hom-Lie algebra and group-like elements, Journal of Pure and Applied Algebra, 222 (5), 2018 , 1139-1163.
[20] U.C. Liang., Q.F. Tian., M. Yao., and S. Ripan On Homgroups and Hm-group Actions, Acta Mathematica, English Series, 39, 2023 , 1887-1906. https://doi.org/10.1007/s10114-023-2133-7, http://www.ActaMath.com.
[21] F. Smarandache, Neutrosophy, Neutrosophic Probability,. Set, and Logic, ProQuest Information and Learning, Ann Arbor, Michigan, USA, 105 p. http://fs.unm.edu/eBook-Neutrosophic6.pdf (edition online), 1998
[22] F. Smarandache, (T,I,F)- Neutrosophic Structures, Neutrosophic Sets and Systems (NSS), 8, 2015, 3-10.
[23] F. Smarandache, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers. In Symbolic Neutrosophic Theory, Chapter 7, Europa Nova, Brussels, Belgium, 2015 ,186-193.
[24] W.B. Vasantha Kandasamy., and F. Smarandache, Neutrosophic Rings, Hexis, Phoenix, Arizona. http://fs.unm.edu/NeutrosophicRings.pdf, 2006
[25] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (2006) , 1965 , 338-353.
[26] A.A.A Agboola A.A.A , On Refined Neutrosophic Quotient Groups, International Journal of Neutrosophic Science (IJNS) Vol. 5, No. 2, 2020 , PP. 76-82
[27] M. Hassanzadeh, Lagranges theorem for Hom-groups, Rocky Mountain J. Math., 49, 2019, 773787
[28] Grigore Calugareanu , The total number of subgroups of a finite abelian, group Scientiae Mathematicae Japonicae online, vol. 10, 2003 ,207217
[29] M. Suzuki M, On the lattice of subgroups of nite groups. Trans. Amer. Math. Soc., 70, 1951 , 345-371.
[30] A.A.A. Agboola, Introduction to Neutrosophic Hom-group, J. Mahani Math. Res. ( To appear )
Published
2025-06-24
How to Cite
Adebisi, S. A., & Adetunji, A. P. (2025). THE NEUTROSOPHIC HOM - GROUPS AND NEUTROSOPHIC HOM - SUBGROUPS I. Unilag Journal of Mathematics and Applications, 4(2), 91-105. Retrieved from https://lagjma.unilag.edu.ng/article/view/2632
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Copyright (c) 2024 Sunday Adesina Adebisi, Ajuebishi Patience Adetunji
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