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

Document Type : Original Article

Author

Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Abstract

In the recent paper [A generalization of Taketa's theorem on M-groups, Quaestiones Mathematicae, (2022), https://doi.org/10.2989/16073606.2022.2081632], we give an upper bound 5/2 for the average of non-monomial character degrees of a finite group G, denoted by acdnm(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 acdnm(G)<acdnm(SL2(5))=19/7.

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