On the Structure of Blocks of Characters of Finite Groups
On the Structure of Blocks of Characters of Finite Groups
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有限群特征块的结构
DOI：
10.1007/978-3-662-21571-5_9
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
R. Brauer
中科院分区：
文献类型：
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作者：
R. Brauer
为了使这种方法成功，尽可能多地了解G的特征标表的性质与G的更具组合性质的性质之间的联系是至关重要的。即使就其本身而言，在这个方向上的研究也提供了许多具有挑战性的问题，因此我们的方法围绕着对字符块的研究。它形成了早期工作的延续[3，4]，并将在以后的论文中进行扩展。我们选择一个素数p，将G的元素集划分为不相交的子集，即G的p-截面，并将G的不可约特征标集划分为不相交的子集，即G的p-块。然后，我们将研究固定p-块中的字符对于固定p-截面中的元素的值。G的每个元素x可以唯一地写为aP p-元素xp与~（的中心化子C（~）的p-正则元素r的乘积x= xr，即是不能被p整除的阶的元素r（C（~）的p-正则元素r。一个p-截面S则由G的元素x组成，其p-因子x与a共轭
For the success of this method, it is of decisive importance to know as much as possible about the connections between the properties of the character table of G and properties of G of a more combinatorial nature. Even for its own sake, an investigation in this direction offers many challenging~ roblemso Our approach centers around a study of the blocks of characters. It forms a continuation of earlier work [3, 4], and it will be extended in a later paper. We choose a prime p and partition the set of elements of G into disjoint subsets, the p-sections of G, and we partition the set of irreducible characters of G into disjoint subsets, the p-blocks of G. We shall then study the values of the characters in a fixed p-block for the elements in a fixed p-section. Each element x of G can be written uniquely as the product x= xr of aP p-element xp and a p-re@ ular element r of the centralizer C (~] of~(that is of an element r (C (~] of an order not divisible by p]. A p-section S then consists of the elements x of G whose p-factor x is conjugate to a