In this paper we seek to
describe and investigate a class of LCA groups which appropriately generalizes the
class of finitely cogenerated abelian groups. Of three possible generalizing classes we
finally choose one, which we refer to as the class of compactly cogenerated LCA
groups, as being the most suitable. It turns out that this class is considerably more
complicated than the corresponding class of compactly generated LCA groups. We
give various criteria for an LCA group to be a member of this class, and we describe
several important subclasses. As a result of our investigations we show that a
divisible LCA group which is indecomposable is either compact and connected, or
else is isomorphic to the group of real numbers, a quasicyclic group, or a p-adic
number group.
