Let D be a non-commutative division ring with centre C, and let Δ be a proper division subring not contained in C. In (4) Cartan raised the question: is it ever possible for each inner automorphism of D to induce an automorphism of Δ? As is well-known, Cartan (4, Théorème 4) with the aid of his Galois Theory answered this negatively in case D is a finite dimensional division algebra. Later Brauer (3), and Hua (8), using elegant, elementary methods, extended Cartan's theorem to arbitrary division rings.