Finite Groups with Some Bounded Codegrees

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 ....

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Veröffentlicht in:Acta mathematica Sinica. English series 2024, Vol.40 (7), p.1778-1784
Hauptverfasser: Yang, Dong Fang, Zeng, Yu, Lv, Heng
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Mathematical analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung: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 .
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-024-1236-0