On Some n-Refined Neutrosophic Groups For  3≤ n ≤ 5

Abuobida M. Ahmed Alfahal^1,* , Sara Sawalmeh², Raja Abdullah Abdulfatah³, Yaser Ahmad Alhasan⁴

¹Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

²Mutah University, Faculty of Science, Mutah, Jordan

³Deanship the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

⁴Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia.  

Emails: a.alfahal@psau.edu.sa; Sarahsawalmeh98@gmail.com; r.abdulfatah@psau.edu.sa; y.alhasan@psau.edu.sa

^*Corresponding author:  a.alfahal@psau.edu.sa

Abstract

This paper is dedicated to studying some examples of n-refined neutrosophic groups and their algebraic substructures, where we deal with three different types of them, 3-refined, 4-refined, and 5-refined neutrosophic groups. Also, we present the algebraic structure of many substructures such as 3-refined neutrosophic AH-subgroups and kernels, 4-refined neutrosophic AH-homomorphisms and subgroups, and 5-refined neutrosophic AH-isomorphisms. On the other hand, many related examples will be provided to explain the algebraic concepts and their properties.

Keywords: 3-refined neutrosophic group; 4-refined neutrosophic group; 5-refined neutrosophic group.