University of Isfahan International Journal of Group Theory 2251-7650 3 3 2014 09 01 Splitting of extensions in the category of locally compact abelian groups 39 45 4435 10.22108/ijgt.2014.4435 EN Hossein Sahleh Department of Mathematics University of Guilan Akbar Alijani University of Guilan Journal Article 2013 02 25 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 $\pounds$‎. https://ijgt.ui.ac.ir/article_4435_22e1c3d0e09071cafadb580f175adec2.pdf