Pythagorean Neutrosophic Triplet Groups

Abstract

It is a well-known fact that groups are the only algebraic structures having a single binary 
operation that is mathematically so perfect that it is impossible to introduce a richer structure 
within it. The main purpose of this study is to introduce the notion of the Pythagorean 
neutrosophic triplet (PNT) which is the generalization of neutrosophic triplet (NT). The PNT is an 
algebraic structure of three ordered pairs that satisfy several properties under the binary operation 
(B-Operation) 
"
 "
 . Furthermore, we used the PNTs to introduce the novel concept of a 
Pythagorean neutrosophic triplet group (PNTG). The algebraic structure (AS) of PNTG is different 
from the neutrosophic triplet group (NTG). We discussed some properties, related results, and 
particular 
examples of these novel concepts. We further studied Pythagorean 
neutro-homomorphism, Pythagorean neutro-isomorphism, etc., for PNTGs. Moreover, we 
discussed the main distinctions between the neutrosophic triplet group (NTG) and the PNTG. 

DOI: 10.5281/zenodo.11206321