ABSTRACT
This chapter presents the detailed investigation of locally compact commutative topological groups. All the questions that arise can be answered in full or at least reduced to questions bearing on commutative algebraic groups. Thus the development is such that the reader may become familiar with this portion of duality theory without immersing himself in the details of the proof of the duality theorem in the general locally compact case. Since all groups under consideration are commutative we shall employ the additive notation. The investigation of subgroups and factor groups plays an important role in group theory so it is only natural to wish to determine the character groups of the subgroups and factor groups of a given group G. Thus compact groups and discrete groups occupy a special place in duality theory. A natural question to ask is how it comes about that the group K plays such a special role in duality theory.
