Generalized T-extensions in Locally Compact Abelian Groups

Let £ be the category of all locally compact abelian (LCA) groups. Let GE £ and HCG. The maximal torsion subgroup of G is denoted by tG and the closure of H by H. A proper short exact sequence 0 + A B in £ is said to be a generalized textension if 0 + TAĻtB C +0 is a proper short exact sequence. We show that the set of all generalized t-extensions of a torsion group A E £ by a compact group C E £ is a subgroup of Ext(C, A). We establish conditions under which the generalized t-extensions split.