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 ${\rm acd}_{nm}(G)$, 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 ${\rm acd}_{nm}(G)<{\rm acd}_{nm}(SL_2(5))=19/7$.
Akhlaghi, Z. (2023). A generalization of Taketa's theorem on $\rm M$-groups $\rm II$. AUT Journal of Mathematics and Computing, 4(1), 63-67. doi: 10.22060/ajmc.2022.21781.1108
MLA
Zeinab Akhlaghi. "A generalization of Taketa's theorem on $\rm M$-groups $\rm II$". AUT Journal of Mathematics and Computing, 4, 1, 2023, 63-67. doi: 10.22060/ajmc.2022.21781.1108
HARVARD
Akhlaghi, Z. (2023). 'A generalization of Taketa's theorem on $\rm M$-groups $\rm II$', AUT Journal of Mathematics and Computing, 4(1), pp. 63-67. doi: 10.22060/ajmc.2022.21781.1108
VANCOUVER
Akhlaghi, Z. A generalization of Taketa's theorem on $\rm M$-groups $\rm II$. AUT Journal of Mathematics and Computing, 2023; 4(1): 63-67. doi: 10.22060/ajmc.2022.21781.1108
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