@article {
author = {Akhlaghi, Zeinab},
title = {A generalization of Taketa's theorem on $\rm M$-groups II},
journal = {AUT Journal of Mathematics and Computing},
volume = {4},
number = {1},
pages = {63-67},
year = {2023},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2022.21781.1108},
abstract = {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 $\mathrm{acd}_{nm}(G)< \mathrm{acd}_{nm}(\mathrm{SL}_2(5))=19/7$.},
keywords = {Monomial character,Primitive character,Taketaâ€™ s Theorem,Average degree},
url = {https://ajmc.aut.ac.ir/article_5011.html},
eprint = {https://ajmc.aut.ac.ir/article_5011_0057069c3de974695209b73b6eb0947d.pdf}
}