Finite groups with character degrees of two distinct primes

It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q}-subgroup H and an Abelian normal {p, q}-complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G.