On t-pure and almost pure exact sequences of LCA groups

Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups

“…So, by Theorem 24.30 of [7], F p contains a compact open subgroup K. Now we have the following exact sequence ... → Ext(X, K) → Ext(X, F p ) → Ext(X, F p /K) → 0 (1.2) Since F p is divisible, so Ext(X, F p /K) = 0 (see [5,Theorem 3.4]). Since X is compact and torsion, so by [7,Theorem 25.9], nX = 0 for some positive integer n. Hence, nExt(X, K) = 0 (see [8,Lemma 2.5]). Since (1.2) is exact, so nExt(X, F p ) = 0.…”

“…Since F p is divisible, so Ext(X, F p /K) = 0 (see [5,Theorem 3.4]). Since X is compact and torsion, so by [7, Theorem 25.9], nX = 0 for some positive integer n. Hence, nExt(X, K) = 0 (see [8,Lemma 2.5]). Since (1.2) is exact, so nExt(X, F p ) = 0.…”