ON THE CODEGREES OF STRONGLY MONOLITHIC CHARACTERS OF FINITE GROUPS
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.111, sa.2, ss.283-289, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 111 Sayı: 2
- Basım Tarihi: 2025
- Doi Numarası: 10.1017/s0004972724000935
- Dergi Adı: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.283-289
- İstanbul Üniversitesi Adresli: Evet
Özet
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.