共轭作用的倒数character
The reciprocal character of the conjugation action
摘要：
对于有限群$G$，我们研究了最小正整数$e(G)$，使得从$g\in G$到$e(G)|G:C_G(g)|$的映射是$G$的广义特征标.结果表明，$e(G)$受局部数据的影响很大，但对于非阿贝尔单群，$e(G)$的行为是不规则的.我们将$e(G)$解释为与$G$的特征表相关的某个非负整数矩阵的初等因子。我们的方法适用于Brauer字符也回答了Navarro最近的一个问题：$G$的$p$ -Brauer字符表决定了$|G|_{p'}$。
英文摘要：
For a finite group $G$ we investigate the smallest positive integer $e(G)$ such that the map sending $g\in G$ to $e(G)|G:C_G(g)|$ is a generalized character of $G$. It turns out that $e(G)$ is strongly influenced by local data, but behaves irregularly for non-abelian simple groups. We interpret $e(G)$ as an elementary divisor of a certain non-negative integral matrix related to the character table of $G$. Our methods applied to Brauer characters also answers a recent question of Navarro: The $p$-Brauer character table of $G$ determines $|G|_{p'}$.
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