International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/461 2020 2020 Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria Agboola A.A. A.A.A. 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. 2020 2020 41 47 10.54216/IJNS.060102 https://www.americaspg.com/articleinfo/21/show/461