For an irreducible character $\chi$ of a finite group $G$, the codegree of $\chi$ is defined by $|G:ker\chi |/\chi (1)$. In this note, we show that if a finite solvable group $G$ has an element of order $m$, then $G$ admits an irreducible character of codegree divisible by $m$.

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元素顺序和字符代码

对于不可约字符 $\chi$ 有限群的 $G$, 的代号 $\chi$ 定义为 $|G：克\chi |/\chi (1)$. 在本笔记中，我们证明如果一个有限可解群$G$ 有秩序元素 $米$， 然后 $G$ 承认代码的不可约特征，可被整除 $米$.