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| Paper IPM / M / 18338 |
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| Abstract: | |
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Let ${\rm acd}(G)$ be the average character degree of a finite group $G$. It has been proved that $\min\{{\rm acd}(G)\mid G\in\mathcal{A}\}=
{\rm acd}(\Al_5)=\frac{16}{5}$, where $\mathcal{A}$ is the family of all finite nonsolvable groups.
In this paper, we assume that $\mathcal{B}$ is the family of all finite nonsolvable groups $G$
having a nonabelian minimal normal subgroup not isomorphic to $\Al_5$.
We prove that $\min\{{\rm acd}(G)\mid G\in\mathcal{B}\}=
{\rm acd}({\rm PSL}(2,7))=\frac{14}{3}$. While we show that the second minimum average
character degree of arbitrary nonsolvable groups does not exist, we classify
all finite groups with ${\rm acd}(G)<14/3$.
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