Splitting of extensions in the category of locally compact abelian groups

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 $0to Xto Yto Gto 0$ with divisible, $sigma-$compact $X$ in $pounds$ splits. We also determine the discrete or compactly generated LCA groups $H$ such that every pure extension $0to Hto Yto Xto 0$ splits for each divisible group $X$ in $pounds$.

Keywords

• Locally compact abelian group
• Splitting of Extension
• Divisible group