Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24494120230201A generalization of Taketa's theorem on $\rm M$-groups II6367501110.22060/ajmc.2022.21781.1108ENZeinabAkhlaghiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranJournal Article20220917In 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 $\mathrm{acd}_{nm}(G)< \mathrm{acd}_{nm}(\mathrm{SL}_2(5))=19/7$.https://ajmc.aut.ac.ir/article_5011_0057069c3de974695209b73b6eb0947d.pdf