Let Formula: see text be a finite group. For a complex irreducible character Formula: see text of Formula: see text, the number Formula: see text is called the codegree of Formula: see text. Our aim here is to study the relationship between the structure of Formula: see text and the codegrees of real-valued strongly monolithic characters of Formula: see text. We obtain new bounds on the Formula: see text-length of a Formula: see text-solvable group, as well as new solvability criteria using the codegrees of real-valued strongly monolithic characters.
Erkoç et al. (Thu,) studied this question.