Volume 6 • Issue 1 • PP: 41-47 • 2020
Introduction to NeutroGroups
Open Access & Copyright
© 2020 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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.
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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,Volume 4 , Issue 1, pp. 16-19 , 2020.
[2] 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.
[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.
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