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ON THE CODEGREES OF STRONGLY MONOLITHIC CHARACTERS OF FINITE GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 111 / Issue 2 / April 2025
- Published online by Cambridge University Press:
- 07 November 2024, pp. 283-289
- Print publication:
- April 2025
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- Article
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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.
