关于余度与Taketa不等式的注记
A note on codegrees and Taketa's inequality
摘要：
设$G$是一个有限群，${\rm cd}(G)$是$G$的复不可约特征标的度的集合.也令${\rm cod}(G)$是$G$的不可约特征标的余度集。Taketa问题证明了如果$G$是可解的，则${\rm dl}(G) \leq |{\rm cd}(G)|$，其中${\rm dl}(G)$是$G$的导出长度。本文证明了${\rm dl}(G) \leq |{\rm cod}(G)|$在某些情况下成立，并猜想当$G$是有限可解群时，这个不等式成立.
英文摘要：
Let $G$ be a finite group and ${\rm cd}(G)$ will be the set of the degrees of the complex irreducible characters of $G$. Also let ${\rm cod}(G)$ be the set of codegrees of the irreducible characters of $G$. The Taketa problem conjectures if $G$ is solvable, then ${\rm dl}(G) \leq |{\rm cd}(G)|$, where ${\rm dl}(G)$ is the derived length of $G$. In this note, we show that ${\rm dl}(G) \leq |{\rm cod}(G)|$ in some cases and we conjecture that this inequality holds if $G$ is a finite solvable group.
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