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
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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| Style | # |
|---|---|
| MLA | S. A. Adebisi,Florentin Smarandache. "The NILPOTENT Characterization of the finite neutrosophic p-groups." International Journal of Neutrosophic Science, Vol. 19, No. 1, 2022 ,PP. 384-388. |
| APA | S. A. Adebisi,Florentin Smarandache. (2022). The NILPOTENT Characterization of the finite neutrosophic p-groups. International Journal of Neutrosophic Science, 19 ( 1 ), 384-388. |
| Chicago | S. A. Adebisi,Florentin Smarandache. "The NILPOTENT Characterization of the finite neutrosophic p-groups." International Journal of Neutrosophic Science, 19 no. 1 (2022): 384-388. |
| Harvard | S. A. Adebisi,Florentin Smarandache. (2022). The NILPOTENT Characterization of the finite neutrosophic p-groups. International Journal of Neutrosophic Science, 19 ( 1 ), 384-388. |
| Vancouver | S. A. Adebisi,Florentin Smarandache. The NILPOTENT Characterization of the finite neutrosophic p-groups. International Journal of Neutrosophic Science, (2022); 19 ( 1 ): 384-388. |
| IEEE | 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) |