aspg-21-461-1791472073 20261008150753 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2020 6 1 Agboola A.A.A. Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria 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 41 47 461 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.060102 https://www.americaspg.com/journal/21/article/461 https://www.americaspg.com/storage/2153.pdf