Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3290 2022 2022 Cape Peninsula University of Technology, Faculty of Applied Science, South Africa admin admin This paper is dedicated to finding all 4-cyclic refined neutrosophic real solutions of the equation 𝑋𝑛=1 which are called 4-cyclic refined real roots of unity. Also, we classify the algebraic group of these solutions as a direct product of some familiar finite cyclic groups. On the other hand, we illustrate many examples to clarify the validity of our work. 2024 2024 28 36 10.54216/GJMSA.0110204 https://www.americaspg.com/articleinfo/33/show/3290