Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3832 2022 2022 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Lee Lee Cape Peninsula University of Technology, Faculty of Applied Science, South Africa Olalekan Joosati In this paper, we study the group of units problem of three different non-commutative logical extensions rings, where we classify the group of units of the rings (NCR)_(Z_pq ), (NCR)_(Z_(2^n ) )and (NCR)_(Z_(p^2 ) )as semi direct products of well-known abelian groups as the following: U(N⊂R)_(Z_pq )≅(Z_(p-1)×Z_(q-1) )∝[(Z_p×Z_q )∝(Z_(p-1)×Z_(q-1)), U(NCR)_(Z_(2^n ) )≅(Z_2×Z_(2^(n-2)))∝(Z_(2^n )∝(Z_2×Z_(2^(n-2)))),   U(N⊂R)_(Z_(p^2 ) )≅Z_(p^2-p)∝(Z_(p^2 )∝Z_(p^2-p)). 2025 2025 19 23 10.54216/GJMSA.0120103 https://www.americaspg.com/articleinfo/33/show/3832