Published 2023-12-31
Keywords
- Multigroup, Submultigroup, Commutator Submultigroups.
How to Cite
Michael, B. D., & Ibrahim, M. A. (2023). Properties of Commutator Submultigroups. Kristu Jayanti Journal of Computational Sciences (KJCS), 3(1), 23–29. https://doi.org/10.59176/kjcs.v3i1.2292
Abstract
This paper vividly studies the properties of commutator in multigroups. It was shown that a commutator submultigroup is commutative and normal. Further, we show that the commutator of the homomorphic image equals the image of the commutator and the result also holds for the inverse image.
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References
[1] A. M. Ibrahim and P. A. Ejegwa, “Characteristics submultigroups of a multigroup.”Gulf J. Math,.vol.5,no.4,(2017), pp.1-8.
[2] A. Syropulous, “Mathematics of multisets,” Springer Verlag, Berlin Heidelberg,. (2001),pp.347-358.
[3] D. Singh, A. M. Ibrahim, T. Yohanna and J. N. Singh, “An overview of the application of multisets,” Novi Sad J. Math., vol.33, no.2,(2007),pp. 73-92.
[4] I. M. Adamu, Y. Tella and A. J. Alkali, “On normal and soft normal groups under multisets and soft multiset context”, MAYFEB Journal of Mathematics, vol.2, (2017),pp.34-47.
[5] J. A. Awolola and A. M. Ibrahim, “Some results on multigroups Quasi Related Syst”. vol.24,no.2(2016),pp. 169-177.
[6] N. J. Wildberger , “A new look at multisets”, School of mathematics, UNSW Sydney 2052, Australia,(2003).
[7] P. A. Ejegwa and A. M. Ibrahim, “On comultisets and factor multigroups”, Theory Appl. Math. Computer Sci.,vol. 7, no.2 (2017), pp.124-140.
[8] P. A. Ejegwa and A. M. Ibrahim, “Direct product of multigroups and its generalization”, Int. J. Math.Combin, vol.4,(2017)pp.1-18.
[9] P. A. Ejegwa and A. M. Ibrahim, “Some homomorphic properties of multigroups”, Bul. Acad. Stiinte Repub. Mold Mat, vol.83,no.1, (2017)pp.67-76.
[10] P. A. Ejegwa and A. M. Ibrahim, “Some group’s analogues results in multigroup setting”, Annals of Fuzzy Mathematics and Informatics, vol.17,(2019),pp. 231-245.
[11] P. A. Ejegwa, and A. M. Ibrahim, “Normal submultigroup and comultiset of a multigroups”, Quasigroups Related System, vol.25, no 2,(2017) pp. 231-244.
[12] S. K. Nazmul, P. Majumdar and S. K. Samanta, “On multisets and multigroups”, Annals of Fuzzy Mathematics and Informatics, vol.6, no.3,(2013)pp. 643-656.
[13] A. M. Ibrahim and P. A. Ejegwa, “A survey on the concept of multigroups”, Journal of the Nigerian Association of Mathematical Physics,vol. 38,(2016)pp. 1-8.
[14] A. M. Ibrahim and P. A. Ejegwa, “Multigroup action on multiset”, Annals of Fuzzy Mathematics and Informatics, vol.14, no.5,(2017)pp. 515-526.
[15] J. A. Awolola and M. A. Ibrahim, “on some algebraic properties of order of an element of a multigroup”, Quasigroups and Related System, vol.25(2017)pp.21-26. 2017.
[16] J.A. Awolola, “On cyclic multigroup family”, Ratio Mathematica, vol.37(2019)pp.61-68.
[2] A. Syropulous, “Mathematics of multisets,” Springer Verlag, Berlin Heidelberg,. (2001),pp.347-358.
[3] D. Singh, A. M. Ibrahim, T. Yohanna and J. N. Singh, “An overview of the application of multisets,” Novi Sad J. Math., vol.33, no.2,(2007),pp. 73-92.
[4] I. M. Adamu, Y. Tella and A. J. Alkali, “On normal and soft normal groups under multisets and soft multiset context”, MAYFEB Journal of Mathematics, vol.2, (2017),pp.34-47.
[5] J. A. Awolola and A. M. Ibrahim, “Some results on multigroups Quasi Related Syst”. vol.24,no.2(2016),pp. 169-177.
[6] N. J. Wildberger , “A new look at multisets”, School of mathematics, UNSW Sydney 2052, Australia,(2003).
[7] P. A. Ejegwa and A. M. Ibrahim, “On comultisets and factor multigroups”, Theory Appl. Math. Computer Sci.,vol. 7, no.2 (2017), pp.124-140.
[8] P. A. Ejegwa and A. M. Ibrahim, “Direct product of multigroups and its generalization”, Int. J. Math.Combin, vol.4,(2017)pp.1-18.
[9] P. A. Ejegwa and A. M. Ibrahim, “Some homomorphic properties of multigroups”, Bul. Acad. Stiinte Repub. Mold Mat, vol.83,no.1, (2017)pp.67-76.
[10] P. A. Ejegwa and A. M. Ibrahim, “Some group’s analogues results in multigroup setting”, Annals of Fuzzy Mathematics and Informatics, vol.17,(2019),pp. 231-245.
[11] P. A. Ejegwa, and A. M. Ibrahim, “Normal submultigroup and comultiset of a multigroups”, Quasigroups Related System, vol.25, no 2,(2017) pp. 231-244.
[12] S. K. Nazmul, P. Majumdar and S. K. Samanta, “On multisets and multigroups”, Annals of Fuzzy Mathematics and Informatics, vol.6, no.3,(2013)pp. 643-656.
[13] A. M. Ibrahim and P. A. Ejegwa, “A survey on the concept of multigroups”, Journal of the Nigerian Association of Mathematical Physics,vol. 38,(2016)pp. 1-8.
[14] A. M. Ibrahim and P. A. Ejegwa, “Multigroup action on multiset”, Annals of Fuzzy Mathematics and Informatics, vol.14, no.5,(2017)pp. 515-526.
[15] J. A. Awolola and M. A. Ibrahim, “on some algebraic properties of order of an element of a multigroup”, Quasigroups and Related System, vol.25(2017)pp.21-26. 2017.
[16] J.A. Awolola, “On cyclic multigroup family”, Ratio Mathematica, vol.37(2019)pp.61-68.