SPLITTING OF EXTENSIONS IN THE CATEGORY OF LOCALLY COMPACT ABELIAN GROUPS

Let $ be the category of all locally compact abelian (LCA) groups. In this paper, the groups G in $ are determined such that every extension 0 ! X ! Y ! G ! 0 with divisible, ??compact X in $ splits. We also determine the discrete or compactly generated LCA groups H such that every pure extension 0 ! H ! Y ! X ! 0 splits for each divisible group X in $.