ON THE CODEGREES OF STRONGLY MONOLITHIC CHARACTERS OF FINITE GROUPS

Abstract Let G be a finite group and let $\chi $ be an irreducible character of G . The number $|G:\mathrm {ker}\chi |/\chi (1)$ is called the codegree of the character $\chi $ . We provide several relations between the structure of G and the codegrees of the characters in a given subset of $\mathrm {Irr}(G)$ , where $\mathrm {Irr}(G)$ is the set of all complex irreducible characters of G . For example, we show that if the codegrees of all strongly monolithic characters of G are odd, then G is solvable, analogous to the well-known fact that if all irreducible character degrees of a finite group are odd, then that group is solvable.