Erratum to : A generalization of Taketa's Theorem on M-groups

TL;DR

This paper corrects and refines a previous result on the average non-monomial character degrees of finite groups, establishing a new sharp bound that guarantees the group's solvability.

Contribution

It introduces a new bound for acdnm(G) ensuring solvability and provides an example demonstrating the bound's sharpness.

Findings

New bound for acdnm(G) established as 19/7

Proves that acdnm(G) < 19/7 implies G is solvable

Provides an example confirming the bound's sharpness

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.