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International Journal of Neutrosophic Science
Volume 19 , Issue 1, PP: 384-388 , 2022 | Cite this article as | XML | Html |PDF


The NILPOTENT Characterization of the finite neutrosophic p-groups

Authors Names :   S. A. Adebisi   1 *     Florentin Smarandache   2  

1  Affiliation :  Department of Mathematics, Faculty of Science, University of Lagos, Nigeria

    Email :  adesinasunday@yahoo.com

2  Affiliation :  University of New Mexico, Gallup Campus, NM 87301, USA

    Email :  smarand@unm.edu

Doi   :   https://doi.org/10.54216/IJNS.190134

Received: March 21, 2022 Accepted: September 05, 2022

Abstract :

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.

Keywords :

Neutrosophic p-groups ; Nilpotency; central series , order; commutator; abelian

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Cite this Article as :
S. A. Adebisi , Florentin Smarandache, The NILPOTENT Characterization of the finite neutrosophic p-groups, International Journal of Neutrosophic Science, Vol. 19 , No. 1 , (2022) : 384-388 (Doi   :  https://doi.org/10.54216/IJNS.190134)