Character degrees in π-separable groups

If a group G is π-separable, where π is a set of primes, the set of irreducible characters Bπ(G) ∪ Bπ′(G) can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito-Michler and Thompson's theorem on character degrees, involving irreducible characters in the set Bπ(G) ∪ Bπ′(G).