A generalization of Taketa's theorem on $\rm M$-groups II

	A generalization of Taketa's theorem on $\rm M$-groups II
AUT Journal of Mathematics and Computing
مقاله 7، دوره 4، شماره 1، 2023، صفحه 63-67 اصل مقاله (337.67 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21781.1108
نویسنده
Zeinab Akhlaghi^*
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
چکیده
In the recent paper [A generalization of Taketa's theorem on $M$-groups, Quaestiones Mathematicae, (2022)], we give an upper bound $5/2$ for the average of non-monomial character degrees of a finite group $G$, denoted by $\mathrm{acd}_{nm}(G)$, which guarantees the solvability of $G$. Although the result is true, the example we gave to show that the bound is sharp turns out to be incorrect. In this paper we find a new bound and we give an example to show that this new bound is sharp. Indeed, we prove the solvability of $G$, by assuming $\mathrm{acd}_{nm}(G)< \mathrm{acd}_{nm}(\mathrm{SL}_2(5))=19/7$.
کلیدواژه‌ها
Monomial character؛ Primitive character؛ Taketa’ s theorem؛ Average degree
مراجع

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