关于正常子群的 $G$ 字符表

arXiv - MATH - Group Theory Pub Date : 2024-09-17 DOI:arxiv-2409.11591

María José Felipe, María Dolores Pérez-Ramos, Víctor Sotomayor

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引用次数: 0

摘要

设 $N$ 是有限群 $G$ 的正则子群。根据布劳尔（Brauer）的一个结果，可以推导出 $G$ 的字符表包含由 $N$ 中元素的 $G$ 共轭类和 $N$ 不可还原字符的 $G$ 轴所诱导的平方次矩阵。在本文中，我们通过群代数的结构为这一事实提供了另一种方法。我们还证明了这种矩阵是非奇异矩阵，并成为从 $G$ 字符表中获取 $N$ 信息的有用工具。

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On $G$-character tables for normal subgroups

Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the $G$-orbits of irreducible characters of $N$. In the present paper, we provide an alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool to obtain information of $N$ from the character table of $G$.

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arXiv - MATH - Group Theory

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