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

• Published in: Symmetry (Basel) Vol. 10; no. 6; p. 194
• Main Authors: W.B., Vasantha, Kandasamy, Ilanthenral, Smarandache, Florentin
• Format: Journal Article
• Language: English
• Published: MDPI AG 01.06.2018
• Subjects: classical group of neutrosophic triplets; neutrosophic triplet groups; pseudo primitive elements; S-semigroup of neutrosophic triplets; semi-neutrosophic triplets; semigroup
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym10060194

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 .