Abstract

In this paper we study the neutrosophic triplet groups for $a\in Z_{2p}$ and prove this collection of triplets $\left(a,neut\left(a\right),anti\left(a\right)\right)$ 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 $Z_{2p}$ 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 $Z_{2p}$ and take only the usual product modulo $2p$ . View Full-Text