421 213
Full Length Article
Volume 6 , Issue 1, PP: 41-47 , 2020

Title

Introduction to NeutroGroups

Authors Names :   Agboola A.A.A.   1 *  

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

    Email :  agboolaaaa@funaab.edu.ng



Doi   :  10.5281/zenodo.3840761


Abstract :

The objective of this paper is to formally present the concept of NeutroGroups by considering three NeutroAxioms (NeutroAssociativity, existence of NeutroNeutral element and existence of NeutroInverse element). Several interesting results and examples of NeutroGroups, NeutroSubgroups, NeutroCyclicGroups, NeutroQuotientGroups and NeutroGroupHomomorphisms are presented. It is shown that generally, Lagrange’s theorem and 1st isomorphism theorem of the classical groups do not hold in the class of NeutroGroups.

Keywords :

Neutrosophy , NeutroGroup , NeutroSubgroup , NeutroCyclicGroup , NeutroQuotientGroup and NeutroGroupHomomorphism.

References :

[1]  Agboola A.A.A., Ibrahim M.A. and Adeleke E.O.,”Elementary Examination of NeutroAlgebras andAntiAlgebras viz-a-viz the Classical Number Systems”, International Journal of Neutrosophic Science,Volume 4 , Issue 1, pp. 16-19 , 2020.

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

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

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