Splitting of extensions in the category of locally compact abelian groups
نویسندگان
1 Damghan University
2 Gonbad-e Qabus University
doi
10.22108/ijgt.2014.4435چکیده
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 $\pounds$.
