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

Zeinab Akhlaghi

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arXiv · 2109.04251

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

Zeinab Akhlaghi

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Abstract

Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average character degree of irreducible characters in 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 character degree of irreducible characters in Irr(G|N) is strictly less than 16=5. We show that the bounds are sharp.

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Zeinab Akhlaghi. 2021-09-09. On the average character degree of some irreducible characters of a finite group. https://arxiv.org/abs/2109.04251

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