On component extensions locally compact abelian groups

Document Type : Research Paper


Department of Mathematics, University of Guilan


Let $\pounds$ be the category of locally compact abelian groups and $A,C\in \pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. We also gives a necessary condition for an LCA group to be component injective in $\pounds$.