Splitting of Closed Subgroups of Locally Compact Abelian Groups
Keywords:Split, Split Full, Locally Compact Abelian Groups
Let £ be the category of all locally compact abelian (LCA) groups. In this paper, we investigate the splitting of the identity component, the subgroup of all compact elements and the maximal torsion subgroup of a group £. A group £ will be called split full if every closed subgroup of G splits. In this paper, we give a necessary condition for an LCA group to be split full.