ON COMPONENT EXTENSIONS OF LOCALLY COMPACT ABELIAN GROUPS

Let £ be the category of locally compact abelian groups and A, C ∈ £. 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 £.