Finite Groups with Some Bounded Codegrees.

For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)2/cod(χ), when χ varies among the irreducible characters of G. [ABSTRACT FROM AUTHOR]