The π-character theory of solvable groups
The π-character theory of solvable groups
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DOI：
10.1017/s1446788700036077
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发表时间：
1994-08
期刊：
影响因子：
--
通讯作者：
I. Isaacs
中科院分区：
文献类型：
--
作者：
I. Isaacs
摘要 有限可解群的普通特征理论有比乍一看更深层的结构。这种结构的莫赫对于一般有限群没有类似物，当从特定素数集合 π 的角度来看可解群的特征时，它就变得可见。这篇纯粹的说明性论文讨论了 π 理论的基础及其一些应用。其中包括 Gajendragadkar 的 π 特殊字符的定义和基本属性，以及它们与不可约 π 部分字符及其相关 Fong 字符的联系。这里讨论的理论的结果包括对有关字符值生成的域、子群字符的扩展和 M 群问题的应用。
Abstract There is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Mauch of this structure, which has no analog for general finite gruops, becomes visible onyl when the character of solvable groups are viewes from the persepective of a particular set π of prime numbers. This purely expository paper discusses the foundations of this πtheory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's π-special characters and their connections with the irreducible πpartial characters and their associated Fong characters. Included among the consequences of the theory discussed here are applications to questions about the field generated by the values of a character, about extensions of characters of subgroups and about M-groups.