Pure extensions of locally compact abelian groups

2005/08/15 by Peter Loth, Loth, Peter · 1 citation
Mathematics · #20K25 #20K35 #20K40 #20K45 (Secondary) #22B05 (Primary) #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0508263

openalex publication_date 2005/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting K denote the class of LCA groups which can be written as the topological direct sum of a compactly generated group and a discrete group, we determine the groups G in K which are pure injective in the category of LCA groups. Finally we describe those groups G in K such that every pure extension of G by a group in K splits and obtain a corresponding dual result.

Cited by

• Applications of Borel-definable homological algebra to locally compact groups

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