Splitting of extensions in the category of locally compact abelian groups

Document Type: Research Paper

Authors

1 Department of Mathematics University of Guilan

2 University of Guilan

Abstract

Let $\pounds$ be the category of all locally compact abelian (LCA) groups‎. ‎In this paper‎, ‎the groups $G$ in $\pounds$ are determined such that every extension $0\to X\to Y\to G\to 0$ with divisible‎, ‎$\sigma-$compact $X$ in $\pounds$ splits‎. ‎We also determine the discrete or compactly generated LCA groups $H$ such that every pure extension $0\to H\to Y\to X\to 0$ splits for each divisible group $X$ in $\pounds$‎.

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