aspg-21-2255-1791475890 20261008161130 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 V. Dhanya Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, India M. Selvarathi Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, India M. Ambika Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, India Neutrosophic set has been developed as a mathematical method for procuring indeterminate and incomplete information. Neutrosophic fuzzy set is a powerful generic system that has been recently developed. In several areas, including data and information analysis, data science, information and decision, have successfully applied neutrosophic concept. Not just that but also the important problems we experience in variety of fields, such as computing, life science, social development, and technical work are represented by neutrosophic fuzzy sets. In this paper, we have presented the idea of an implication-based (ȷρ) neutrosophic fuzzy (F) subgroup over a finite group and a ȷρ neutrosophic F normal subgroup over a finite group. Further, we have established a few fundamental properties of a ȷρ neutrosophic F subgroup over a finite group and ȷρ neutrosophic F normal subgroup over a finite group. 2024 146 154 2255 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230113 https://www.americaspg.com/journal/21/article/2255 https://www.americaspg.com/storage/11737499350.pdf