Introduction to NeutroGroups
Agboola A.A. A.A.A.
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.
Topics & Concepts
Element (criminal law)Class (philosophy)MathematicsIsomorphism (crystallography)Isomorphism theoremPure mathematicsAlgebra over a fieldMaximal elementCalculus (dental)Computer sciencePolitical scienceLawArtificial intelligenceProgramming languageCrystal structureChemistrySet (abstract data type)MedicineDentistryCrystallographyAdvanced Algebra and LogicFuzzy and Soft Set TheoryRough Sets and Fuzzy Logic