ON THE CODEGREES OF STRONGLY MONOLITHIC CHARACTERS OF FINITE GROUPS

Erkoç T., Yılmaztürk U.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1017/s0004972724000935
  • Dergi Adı: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • 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.