Year: 2024
Type: article
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.
Authors: TEMHA ERKOÇ, UTKU YIlMAZTÜRK
Institution: Istanbul University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
Award: G489277897
OpenAlex ID: W4404155895