The Construction and Reconstruction of the Neutrosophic Hom-Groups and Neutrosophic Hom-Subgroups from the Indigenous and Primitive Hom-Group
Keywords:
Hom-groups, Hom-subgroups, Neutrosophic groups, Neutrosophic subgroups, Neutrosophic hom-groups, Neutrosophic homsubgroups
Abstract
Hom-groups are the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. The neutrosophic 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, we have been able to give some introductory entities on the concept of both Hom-groups as well as the neutrosophic Hom-groups; our utmost aim is to construct neutrosophic Hom-group and neutrosophic Hom-subgroups from the already known Hom-groups.
References
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Jiang, J., Mishra, S.K., and Sheng, Y., Hom-Lie algebras and Hom-Lie groups, integration and differentiation. SIGMA Symmetry Integrability Geom. methods Appl., 16 (137), 2020, 22.
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Calugareanu, G., The total number of subgroups of a finite abelian group, Scientiae Mathematicae Japonicae online, vol. 10, 2003, 207-217.
Suzuki, M., On the lattice of subgroups of finite groups. Trans. Amer. Math. Soc., 70, 1951, 345-371.
Agboola, A.A.A., Introduction to Neutrosophic Hom-group, J. Mahani Math. Res. (To appear)
Vasantha Kandasamy, W.B., and Smarandache F., Neutrosophic Rings, Hexis, Phoenix, Arizona, 2006.
Ali, R., Neutrosophic Matrices and Their Properties, Cairo University, Cairo, Egypt.
Suzuki, M., On the lattice of subgroups of finite groups. Trans. Amer. Math. Soc., 70, (1951), 345-371.
Judson, T.W., Abstract Algebra Theory and Applications University of Puget Sound, (2015).
Ayinde, S.A., Approximate Identities in Algebras of Compact Operators on Frechet Spaces, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 7, No. 2, (2022) pp. 129-139.
Adetunji, A., et al., Impacts of Slips on Peristaltic Flow and Heat Transfer of Micropolar Fluids in an Asymmetric Channel, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 7, No. 2, (2022) pp. 107-128.
Fatunmi, E.O., Mabood, F. and Adeniyan, A., Stagnation-Point Flow of Magneto-Williamson Nanofluid over a Stretching Material with Ohmic Heating and Entropy Analysis. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 7, (2021), 131-145.
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Babayo, A. M., et al., On the Digraphic Decomposition of Stable Quasi-Idempotents within Finite Partial Transformation Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(1), (2025), Pages 11-23.
Ibrahim, A., Nwaibeh, E. A., Francis, M. O., and Okigbo, C. J., On collapse of order preserving and idempotent of order-preserving full contraction transformation semigroup. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(2): (2024). 1-8.
Imam, A. T., Usman, L., Idris, A., and Ibrahim, S., Product of quasi-idempotents in a finite semigroup of partial order-preserving transformations. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1): (2024). 53-59.
Ilojide, E. and George, O. O., Hyper-Homomorphisms in Obic Algebras, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 2025, Pages 19-28.
Francis, M. O., Adeniji, A. O., Mogbonju, M. M., Workdone by m-Topological Transformation Semigroup, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1) (2023), 33-42.
Ali, B., et al., On Quasi-Nilpotents in Finite Partial Transformation Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 2025, Pages 55-61.
Ali, B., Jada, M. A., Zubairu, M. M., On Rank of Semigroup of Order-Preserving Order-Decreasing Partial Contraction Mappings on a Finite Chain. International Journal of Mathematical Sciences and Optimization: Theory and Applications 10(4): (2024). 1-11.
Agboola, A.A.A., Akinola., A.D., and Oyebola, O.Y., Neutrosophic Rings I, Int. J. of Math. Comb., 4, 2011, 1-14.
Agboola, A.A.A., Adeleke., E.O., and Akinleye, S.A., Neutrosophic Rings II, Int. J. of Math. Comb., 2, 2012, 1-8.
Agboola, A.A.A., On Refined Neutrosophic Algebraic Structures, Neutrosophic Sets and Systems (NSS), 10, 2015 99-101.
Agboola., A.A.A., and Davvaz., B., On Neutrosophic Canonical Hypergroups and Neutrosophic Hyperrings, Neutrosophic Sets and Systems (NSS), 2, 2014, 34-41.
Agboola, A.A.A., Davvaz., B., and Smarandache, F., Neutrosophic Quadruple Hyperstructures, Annals of Fuzzy Mathematics and Informatics, 14, 2017, 29-42.
Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., Refined Neutrosophic Rings I, International Journal of Neutrosophic Science (IJNS), 2 (2), 2020, 77-81.
Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., Refined Neutrosophic Rings II, International Journal of Neutrosophic Science (IJNS), 2 (2), 2020, 89-94.
Akinleye, S.A., Smarandache, F., and Agboola, A.A.A., On Neutrosophic Quadruple Algebraic Structures, Neutrosophic Sets and Systems (NSS), 12, 2016, 122-126.
Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems (FSS), 20, 1986, 87-96.
Gilbert, I. and Gilbert, J., Elements of Modern Algebra, Eight Edition, Cengage Learning, USA, 2015.
Hartwig, J.T., Larson., D., and Silvestrov, S.D., Deformations of Lie Algebras using - derivations, J. Algebra, 295, 2006, 314-361.
Hassanzadeh, M., Lagrange's theorem for Hom-groups, Rocky J.Math., 49, 2019, 773-787.
Hassanzadeh, M., Hom-groups, representations and homological algebra, Colloq. Math., 158, 2019, 21-38.
Ibrahim, M.A., Agboola, A.A.A., Adeleke, E.O., and Akinleye, S.A., Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup International Journal of Neutrosophic Science (IJNS), 2 (1), 2020, 47-62.
Isaacs, I.M., Finite Group Theory, American Mathematical Society, Providence, RI., 2008.
Jiang, J., Mishra, S.K., and Sheng, Y., Hom-Lie algebras and Hom-Lie groups, integration and differentiation. SIGMA Symmetry Integrability Geom. methods Appl., 16 (137), 2020, 22.
Laurent-Gengouza, C., Makhlouf, A., and Teles, J., Universal algebra of a Hom-Lie algebra and group-like elements, Journal of Pure and Applied Algebra, 222 (5), 2018, 1139-1163.
Liang, U.C., Tian, Q.F., Yao, M., and Ripan, S., On Homgroups and Hom-group Actions, Acta Mathematica, English Series, 39, 2023, 1887-1906.
Smarandache, F., Neutrosophy, Neutrosophic Probability., Set, and Logic, ProQuest Information and Learning, Ann Arbor, Michigan, USA, 1998.
Smarandache, F., (T,I,F)-Neutrosophic Structures, Neutrosophic Sets and Systems (NSS), 8, 2015, 3-10.
Smarandache, F., 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.
Vasantha Kandasamy, W.B., and Smarandache, F., Neutrosophic Rings, Hexis, Phoenix, Arizona, 2006.
Zadeh, L.A., Fuzzy sets, Information and Control, 8, 1965, 338-353.
Agboola, A.A.A., On Refined Neutrosophic Quotient Groups, International Journal of Neutrosophic Science (IJNS) Vol. 5, No. 2, 2020, PP. 76-82.
Hassanzadeh, M., Lagrange's theorem for Hom-groups, Rocky Mountain J. Math., 49, 2019, 773-787.
Calugareanu, G., The total number of subgroups of a finite abelian group, Scientiae Mathematicae Japonicae online, vol. 10, 2003, 207-217.
Suzuki, M., On the lattice of subgroups of finite groups. Trans. Amer. Math. Soc., 70, 1951, 345-371.
Agboola, A.A.A., Introduction to Neutrosophic Hom-group, J. Mahani Math. Res. (To appear)
Vasantha Kandasamy, W.B., and Smarandache F., Neutrosophic Rings, Hexis, Phoenix, Arizona, 2006.
Ali, R., Neutrosophic Matrices and Their Properties, Cairo University, Cairo, Egypt.
Suzuki, M., On the lattice of subgroups of finite groups. Trans. Amer. Math. Soc., 70, (1951), 345-371.
Judson, T.W., Abstract Algebra Theory and Applications University of Puget Sound, (2015).
Ayinde, S.A., Approximate Identities in Algebras of Compact Operators on Frechet Spaces, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 7, No. 2, (2022) pp. 129-139.
Adetunji, A., et al., Impacts of Slips on Peristaltic Flow and Heat Transfer of Micropolar Fluids in an Asymmetric Channel, International Journal of Mathematical Sciences and Optimization: Theory and Applications, Vol. 7, No. 2, (2022) pp. 107-128.
Fatunmi, E.O., Mabood, F. and Adeniyan, A., Stagnation-Point Flow of Magneto-Williamson Nanofluid over a Stretching Material with Ohmic Heating and Entropy Analysis. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 7, (2021), 131-145.
Imam, A. T., et al., Product of Quasi-Idempotents in Finite Semigroup of Partial Order-Preserving Transformations, International Journal of Mathematical Sciences and Optimization: Theory and Applications 10(1), 2024, Pages 53-59.
Babayo, A. M., et al., On the Digraphic Decomposition of Stable Quasi-Idempotents within Finite Partial Transformation Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(1), (2025), Pages 11-23.
Ibrahim, A., Nwaibeh, E. A., Francis, M. O., and Okigbo, C. J., On collapse of order preserving and idempotent of order-preserving full contraction transformation semigroup. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(2): (2024). 1-8.
Imam, A. T., Usman, L., Idris, A., and Ibrahim, S., Product of quasi-idempotents in a finite semigroup of partial order-preserving transformations. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1): (2024). 53-59.
Ilojide, E. and George, O. O., Hyper-Homomorphisms in Obic Algebras, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 2025, Pages 19-28.
Francis, M. O., Adeniji, A. O., Mogbonju, M. M., Workdone by m-Topological Transformation Semigroup, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1) (2023), 33-42.
Ali, B., et al., On Quasi-Nilpotents in Finite Partial Transformation Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 2025, Pages 55-61.
Ali, B., Jada, M. A., Zubairu, M. M., On Rank of Semigroup of Order-Preserving Order-Decreasing Partial Contraction Mappings on a Finite Chain. International Journal of Mathematical Sciences and Optimization: Theory and Applications 10(4): (2024). 1-11.
Published
2026-02-10
How to Cite
Adebisi, S., & Adetunji, A. (2026). The Construction and Reconstruction of the Neutrosophic Hom-Groups and Neutrosophic Hom-Subgroups from the Indigenous and Primitive Hom-Group. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(4), 97 - 113. Retrieved from https://ijmso.unilag.edu.ng/article/view/2918
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