Branch Mathematics and Statistics Faculty and Staff Publications
The NILPOTENT Characterization of the finite neutrosophic p-groups
Document Type
Article
Publication Date
2022
Abstract
A well known and referenced global result is the nilpotent characterisation of the finite p-groups. This un doubtedly 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.
Language (ISO)
English
Keywords
Neutrosophic p-groups, Nilpotency, central series, order, commutator
Recommended Citation
Smarandache, Florentin and S. A. Adebisi. "The NILPOTENT Characterization of the finite neutrosophic p-groups." (2022). https://digitalrepository.unm.edu/math_fsp/613
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
