BG-algebras constructed from a noncommutative group. BG-algebras is a generalization of B-algebras, so some concepts in B-algebras can also be applied in BG-algebras, such as concepts derivations. This thesis uses the method of construction of derivations in B-algebras by Al-Shehrie. The results obtained dene (l; r)-derivations, (r; l)-derivations, and left derivations in BG-algebras, reg…