Character degrees in $\pi$-separable groups

Abstract

If a group $G$ is $\pi$-separable, where $\pi$ is a set of primes, the set of irreducible characters $B_{\pi }(G)\cup B_{{\pi }^{\prime }}(G)$ can be defined. In this paper, we prove that there are variants of some classical theorems in character theory, namely the Theorem of Ito-Michler and Thompson theorem on character degrees, which involve irreducible characters in the set $B_{\pi }(G)\cup B_{{\pi }^{\prime }}(G)$.