Vol. 65, No. 1, 1976

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Compactly cogenerated LCA groups

David Lee Armacost

Vol. 65 (1976), No. 1, 1–12

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.

Mathematical Subject Classification 2000
Primary: 22B05
Received: 26 September 1974
Published: 1 July 1976
David Lee Armacost