Answer to Question #18179 in Abstract Algebra for Mohammad

Question

For any group G, let
Δ(G) = {g ∈ G: [G : CG(g)] < ∞}, and Δ+(G) = {g ∈ Δ(G) : g has finite order}.
Show that Δ(G)/Δ+(G) is torsion-free abelian.