Finite Groups II
Finite Groups II
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DOI：
10.1007/978-3-642-67994-0
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发表时间：
1982-04
期刊：
影响因子：
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通讯作者：
B. Huppert;N. Blackburn
中科院分区：
文献类型：
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作者：
B. Huppert;N. Blackburn
和Dann erst kommt der“ab-ge-sa.Ng‘da./3 der nidlt Kurz and nht zu la.这本书的最后一卷涉及1960年代“S”中的一些发展。在试图确定单群时，第一步是解决Burnside的猜想，即奇数阶群是可解的。这个猜想正确的证明太长太复杂，不适合在本文中提出，但它早期阶段的一些想法导致了有限群的局部理论，因此我在第十章中讨论了它的各个方面。这些讨论的大部分是转移理论的延续(见第四章)，但我们也引入了广义拟合子群，它在刻画定理中起着基本的作用，即仅根据群论性质来描述特定的群。关于Zassenhaus群的刻画是最早也是最重要的刻画之一，见第十一章。根据Brauer和Fowler的定理，用对合的中心子刻画是特别重要的。在第十二章给出了一个这样的定理，刻画了Mathieu群9J‘l1和PSL(3，3
Und dann erst kommt der" Ab-ge-sa. ng\'da./3 der nidlt kurz und nicht zu la. ng, From" Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the 1960's. In attempting to determine the simple groups, the first step was to settle the conjecture of Burnside that groups of odd order are soluble. The proof that this conjecture was correct is much too long and complicated for presentation in this text, but a number of ideas in the early stages of it led to a local theory of finite groups, so me aspects of which are discussed in Chapter X. Much of this discussion is a con tinuation of the theory of the transfer (see Chapter IV), but we also introduce the generalized Fitting subgroup, which played a basic role in characterization theorems, that is, in descriptions of specific groups in terms of group-theoretical properties alone. One of the earliest and most important such characterizations was given for Zassenhaus groups; this is presented in Chapter XI. Characterizations in terms of the centralizer of an involution are of particular importance in view of the theorem of Brauer and Fowler. In Chapter XII, one such theorem is given, in which the Mathieu group 9J'l1l and PSL (3, 3) are characterized