223 139
Full Length Article
Volume 10 , Issue 2, PP: 84-95 , 2020

Title

On Finite NeutroGroups of Type-NG[1,2,4]

Authors Names :   A.A.A. Agboola   1  

1  Affiliation :  Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria.

    Email :  agboolaaaa@funaab.edu.ng



Doi   :  10.5281/zenodo.4006602

Received: May 02, 2020 Accepted: August 20, 2020

Abstract :

 

 

The NeutroGroups as alternatives to the classical groups are of different types with different algebraic prop- erties. In this paper, we are going to study a class of NeutroGroups of type-NG[1,2,4]. In this class of Neu- troGroups, the closure law, the axiom of associativity and existence of inverse are taking to be either partially true or partially false for some elements; while the existence of identity element and axiom of commutativity are taking to be totally true for all the elements. Several examples of NeutroGroups of type-NG[1,2,4] are presented along with their basic properties. It is shown that Lagrange’s theorem holds for some NeutroSub- groups of a NeutroGroup and failed to hold for some NeutroSubgroups of the same NeutroGroup. It is also shown that the union of two NeutroSubgroups of a NeutroGroup can be a NeutroSubgroup even if one is not contained in the other; and that the intersection of two NeutroSubgroups may not be a NeutroSubgroup. The concepts of NeutroQuotientGroups and NeutroGroupHomomorphisms are presented and studied. It is shown that the fundamental homomorphism theorem of the classical groups is holding in the class of NeutroGroups of type-NG[1,2,4].

 

 

 

 

Keywords :

 

Neutrosophy; group; NeutroGroup; AntiGroup; NeutroSubgroup; NeutroCyclicGroup; Neutro- QuotientGroup; NeutroGroupHomomorphism.

 

References :

 

[1]   Agboola, A.A.A., Ibrahim, M.A. and Adeleke, E.O., “Elementary Examination of NeutroAlgebras and AntiAlgebras viz-a-viz the Classical Number Systems”, International Journal of Neutrosophic Science, vol. 4 (1), pp. 16-19, 2020. DOI:10.5281/zenodo.3752896.

 

[2]   Agboola, A.A.A., “Introduction to NeutroGroups”, International Journal of Neutrosophic Science (IJNS),Vol. 6 (1), pp. 41-47, 2020. (DOI: 10.5281/zenodo.3840761).

 

[3]   Agboola, A.A.A., “Introduction to NeutroRings”, International Journal of Neutrosophic Science (IJNS),Vol. 7 (2), pp. 62-73, 2020. (DOI:10.5281/zenodo.3877121).

 

[4]   Akbar, R. and Smarandache, F., “On Neutro-BE-algebras and Anti-BE-algebras (revisited)”, International Journal of Neutrosophic Science (IJNS), Vol. 4 (1), pp. 08-15, 2020. (DOI: 10.5281/zenodo.3751862).

 

[5]   Gilbert, L. and Gilbert, J., “Elements of Modern Algebra”, Eighth Edition, Cengage Learning, USA, 2015.

 

[6]   Smarandache, F., “NeutroAlgebra is a Generalization of Partial Algebra”, International Journal of Neutrosophic Science, vol. 2 (1), pp. 08-17, 2020.

 

[7]   Smarandache, F., “Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)”,Neutrosophic Sets and Systems (NSS), vol. 31, pp. 1-16, 2020. DOI: 10.5281/zenodo.3638232.

 

[8]   Smarandache, F., “Introduction to NeutroAlgebraic Structures”, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Ch. 6, pp. 240-265, 2019.

 

[9]   Smarandache, F. Neutrosophy, Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998. http://fs.unm.edu/eBook-Neutrosophic6.pdf (edition online)