aspg-33-3832-1792223362 20261017074922 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2025 12 1 Lee Xu University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Olalekan Joosati Cape Peninsula University of Technology, Faculty of Applied Science, South Africa 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 19 23 3832 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0120103 https://americaspg.com/journal/33/article/3832 https://americaspg.com/storage/21746130392.pdf