The Structure Theorems for Infinite Abelian Groups

This paper, examines one of the most fundamental and interesting algebraic structures, infinite abelian groups, from the perspective of group theory The Theory of abelian groups is generally simpler than that of their non-abelian counterparts and finite abelian groups are very well understood. Then would like to state whether the theory of Structure for infinite abelian group of additive rational number is finitely generated or a divisible abelian group and also show examples of each classification. Thus, classify groups by stating whether elements are finite or infinite and categories them as infinite abelian Groups. Moreover, an application to homology group and rotation in two dimensions is presented, as a demonstration of the structure of infinite abelian groups utility.