“Group” is understood to mean “abelian group”. Let 2 be the class of all torsion groups. Given any group A the family of subgroups {U ≤ A | A/U ∈ 2} serves as a neighborhood base at 0 ∈ A defining a group topology on A in such a way that every group homomorphism is continuous. Thus the “2-topology” does not add new structure to a group, i.e., A ∼= B as groups if and only if A and B are isomorphic as topological groups, but the topology raises new questions, and introduces related concepts and objects such as completions. The 2-topology is thoroughly investigated in this paper.
