A note on codegrees and Taketa's inequality

Abstract

Let $G$ be a finite group and $\mathrm{cd}(G)$ will be the set of the degrees of the complex irreducible characters of $G$. Also let $\mathrm{cod}(G)$ be the set of codegrees of the irreducible characters of $G$. The Taketa problem conjectures if $G$ is solvable, then $\mathrm{dl}(G)\le |\mathrm{cd}(G)|$, where $\mathrm{dl}(G)$ is the derived length of $G$. In this note, we show that $\mathrm{dl}(G)\le |\mathrm{cod}(G)|$ in some cases and we conjecture that this inequality holds if $G$ is a finite solvable group.

There is a mistake in the proof of lemma 3.1