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On the average degree of some irreducible characters of a finite group

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  • Zeinab Akhlaghi

Abstract

Let G be a finite group and N be a non‐trivial normal subgroup of G, such that the average degree of irreducible characters in Irr(G|N)${\mathrm{Irr}}(G|N)$ is less than or equal to 16/5. Then, we prove that N is solvable. Also, we prove the solvability of G, by assuming that the average degree of irreducible characters in Irr(G|N)${\mathrm{Irr}}(G|N)$ is strictly less than 16/5. We show that the bounds are sharp.

Suggested Citation

  • Zeinab Akhlaghi, 2023. "On the average degree of some irreducible characters of a finite group," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3149-3152, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3149-3152
    DOI: 10.1002/mana.202100440
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