University of IsfahanInternational Journal of Group Theory2251-76503320140901Splitting of extensions in the category of locally compact abelian groups3945443510.22108/ijgt.2014.4435ENHosseinSahlehDepartment of Mathematics
University of GuilanAkbarAlijaniUniversity of GuilanJournal Article20130225Let $\pounds$ 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