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

Zeinab Akhlaghi

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3149-3152

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.

Date: 2023
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https://doi.org/10.1002/mana.202100440

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