Lower defect groups
Lower defect groups
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DOI：
10.1080/00927878008822458
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发表时间：
1980
影响因子：
0.7
通讯作者：
J. B. Olsson
中科院分区：
文献类型：
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作者：
J. B. Olsson
1.十年前，R。布劳尔发表了一篇论文111，在其中他介绍了作为一个自然推广的缺陷群的所谓”低缺陷群”的p-块的有限群。Brauer的公式表明，下亏群的重数连接了有限群的重要性质，它的共轭类，p-截面和p-块。因此，这是有点令人惊讶的是，该文件自那时以来一直被忽视（除了结果[k]，[L]和应用程序在iz！）。其原因可能是，布劳尔的文件是相当难以阅读。G的p-子群作为p-块的下亏群的重数被定义为块理想的对偶空间的子集中的子空间的最大维数，这似乎很难处理。因此，最好给出其他等价的定义，使计算更容易。这里我们使用Rosenberg-Michler方法（参见[E]和[II]）
1. About 10 years ago, R. Brauer published a paper 111, in which he introduced as a natural generalization of defect groups the socalled" lower defect groups" for p-blocks of finite groups. The formulas of Brauer show that multiplicities of lower defecc groups connect important properties of a finite group, its conjugacy classes, p-sections and p-blocks. It is therefore somewhat surprising that the paper since then has been rather neglected (with exception of results in [k],[L] and an application in iz!). The reason for this may be, that Brauer's paper is fairly difficult to read. The multiplicity of a p-subgroup of G as a lower defect group for a p-block is defined as the maximal dimension of a subspace in a subset of the dual space of the block ideal and this appears to be hard to work with. Therefore it is desirable to give other equivalent definitions, which make calculations easier. Here we use a Rosenberg-Michler approach (see [E] and [ll))