Unreduced Generalized Endoprimal Abelian Groups

An endofunction on an Abelian group A is a fonction f: A n → A such that φf ( x 1 , …, x n ) = f ( φ ( x 1 ), …, φ ( x n )) for all endomorphisms φ of group A and all n from ℕ. If each endofunction has the form \(f\left(x_{1}, \ldots, x_{n}\right)=\sum\nolimits_{i=1}^{n} \lambda_{i} x_{i}\) for some central endomorphisms λ 1 , …, λ n of group A , then such a group is called generalized endoprimal ( GE ) group. In this paper, we find GE -groups in the class of nonreduced Abelian groups. In addition, results paper, we find GE-group in the class of nonreduced Abelian groups. In addition, results concerning connections of GE -groups with Abelian groups whose endomorphism rings are unique addition rings have been obtained.