On the Codegrees of Real Strongly Monolithic Characters

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.