Summary: We improve a few results related to Huppert's $\rho $-$\sigma $ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.
[5] Manz, O., Wolf, T. R.: Representations of Solvable Groups. London Mathematical Society Lecture Notes Series 185. Cambridge University Press, Cambridge (1993). DOI 10.1017/CBO9780511525971 | MR 1261638 | Zbl 0928.20008