This final project the properties of BG-algebras and the relationship of BG- algebras with Abelian groups, Coxeter algebras, and BOI-algebras. In this case it can be proven by showing through the properties of BG-algebras related to the properties of Abelian groups, Coxeter algebras, and BOI-algebras, so that some related properties are obtained. In this study it can be seen that every Abelian…