On G-character tables for normal subgroups
On G-character tables for normal subgroups
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关于正规子群的 G 字符表
DOI：
10.2989/16073606.2022.2040633
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
V. Sotomayor
中科院分区：
文献类型：
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作者：
M. J. Felipe;M. D. Pérez;V. Sotomayor
设N是有限群G的正规子群。由Brauer的一个结果可以导出G的特征标表中含有由N中元素的G-共轭类和N的不可约特征标的G-轨道诱导的子方阵。在本文中，我们提供了一个替代的方法，这一事实，通过结构的群代数。我们还证明了这类矩阵是非奇异的，并成为从G的特征标表中获得N的信息的有用工具。
Abstract 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.