Direct Product of Finite Abelian Group

In this project, finite abelian groups with some theoretical and algebraic structures are considered. The order of each group is factorized completely with factor of higher multiplicity where necessary. This unique factorization will allow for a way of building new groups and understanding a given group better. Essentially, it provides a way of relating the given group to the direct products of some of its subgroups. Finally, it also reveals how a group of a finite order is isomorphically related to one of the direct products satisfying certain relatively prime condition.