Extensions of locally compact abelian, torsion-free groups by compact torsion abelian groups

Let \(X\) be a compact torsion abelian group. In this paper, we show that an extension of \(F_{p}\) by \(X\) splits where \(F_{p}\) is the p-adic number group and \(p\) a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by \(X\) is not split.