TY - JOUR
ID - 5011
TI - A generalization of Taketa's theorem on $\rm M$-groups II
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Akhlaghi, Zeinab
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Y1 - 2023
PY - 2023
VL - 4
IS - 1
SP - 63
EP - 67
KW - Monomial character
KW - Primitive character
KW - Taketaâ€™ s Theorem
KW - Average degree
DO - 10.22060/ajmc.2022.21781.1108
N2 - 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 $\mathrm{acd}_{nm}(G)< \mathrm{acd}_{nm}(\mathrm{SL}_2(5))=19/7$.
UR - https://ajmc.aut.ac.ir/article_5011.html
L1 - https://ajmc.aut.ac.ir/article_5011_0057069c3de974695209b73b6eb0947d.pdf
ER -