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Symmetry 2018, 10(6), 194; https://doi.org/10.3390/sym10060194

A Classical Group of Neutrosophic Triplet Groups Using {Z2p, ×}

1
School of Computer Science and Engineering, VIT, Vellore 632014, India
2
Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Received: 15 May 2018 / Revised: 24 May 2018 / Accepted: 25 May 2018 / Published: 1 June 2018
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Abstract

In this paper we study the neutrosophic triplet groups for a Z 2 p and prove this collection of triplets a , n e u t ( a ) , a n t i ( a ) if trivial forms a semigroup under product, and semi-neutrosophic triplets are included in that collection. Otherwise, they form a group under product, and it is of order ( p 1 ) , with ( p + 1 , p + 1 , p + 1 ) as the multiplicative identity. The new notion of pseudo primitive element is introduced in Z 2 p analogous to primitive elements in Z p , where p is a prime. Open problems based on the pseudo primitive elements are proposed. Here, we restrict our study to Z 2 p and take only the usual product modulo 2 p . View Full-Text
Keywords: neutrosophic triplet groups; semigroup; semi-neutrosophic triplets; classical group of neutrosophic triplets; S-semigroup of neutrosophic triplets; pseudo primitive elements neutrosophic triplet groups; semigroup; semi-neutrosophic triplets; classical group of neutrosophic triplets; S-semigroup of neutrosophic triplets; pseudo primitive elements
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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W.B., V.K.; Kandasamy, I.; Smarandache, F. A Classical Group of Neutrosophic Triplet Groups Using {Z2p, ×}. Symmetry 2018, 10, 194.

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