generalized t-extensions in locally compact abelian groups

Let £ be the category of all locally compact abelian (lca) groups. let g ∈ £ and h ⊆ g. the maximal torsion subgroup of g is denoted by tg and the closure of h by h. a proper short exact sequence 0 → a φ→ b ψ→ c → 0 in £ is said to be a generalized textension if 0 → ta φ→ tb ψ→ tc → 0 is a proper short exact sequence. we show that the set of all generalized t-extensions of a torsion group a ∈ £ by a compact group c ∈ £ is a subgroup of ext(c, a). we establish conditions under which the generalized t-extensions split.