A note on the torsion elements in the centralizer of a finite index subgroup (Q2365206)

Let \(H\) be any subgroup of finite index in a given group \(G\) and \(T\) be the set of torsion elements of the centralizer \(C_G(H)\) of \(H\) in \(G\). The author proves that \(T\) is a subgroup of \(G\). Moreover it is shown that if \(H\) is torsion free and normal then \(T\) is the unique maximal normal torsion subgroup of \(G\).