论文标题
共轭动作的相互特征
The reciprocal character of the conjugation action
论文作者
论文摘要
对于有限的组$ g $，我们调查了最小的正整数$ e（g）$，以使地图将$ g \ in G $以$ e（g）发送到$ e（g）| g：c_g（g）| $是$ g $的广义字符。事实证明，$ e（g）$受到本地数据的强烈影响，但对非亚伯利亚简单群体的行为不规则。我们将$ e（g）$解释为与$ g $的字符表相关的某个非负积分矩阵的基本除数。我们适用于Brauer字符的方法还回答了Navarro的最新问题：$ p $ -Brauer字符表$ g $确定$ | g | _ {p'} $。
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 $|G|_{p'}$.
