International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1294 2020 2020 Department of Mathematics, Faculty of Science, University of Lagos, Nigeria S. A. Adebisi University of New Mexico, Gallup Campus, NM 87301, USA Florentin Smarandache A well known and referenced global result is the nilpotent characterisation of the finite p-groups. This undoubtedly transends into neutrosophy. Hence, this fact of the neutrosophic nilpotent p-groups is worth critical studying and comprehensive analysis. The nilpotent characterisation depicts that there exists a derived series (Lower Central) which must terminate at {ϵ} ( an identity ) , after a finite number of steps. Now, Suppose that G(I) is a neutrosophic p-group of class at least m ≥ 3. We show in this paper that Lm−1(G(I)) is abelian and hence G(I) possesses a characteristic abelian neutrosophic subgroup which is not supposed to be contained in Z(G(I)). Furthermore, If L3(G(I)) = 1 such that pm is the highest order of an element of G(I)L2(G(I)) (where G(I) is any neutrosophic p-group) then no element of L2(G(I)) has an order higher than pm. 2022 2022 384 388 10.54216/IJNS.190134 https://www.americaspg.com/articleinfo/21/show/1294