The finite simple groups
The finite simple groups
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DOI：
10.1007/978-1-84800-988-2
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
R. Wilson
中科院分区：
文献类型：
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作者：
R. Wilson
Thisbookisintendedasanintroductiontoallthe吗?nitesimplegroups。在themonumentalstruggletoclassifythe ?自成立以来，已经积累了大量关于这些群体的信息。将这些信息传递给下一代的学生和研究人员，更不用说那些可能希望应用这些知识的人，已经成为一项重大挑战。随着Aschbacher和Smith[12,13]在2004年出版的两卷书，我们可以合理地看待Classi？有限单群的阳离子定理（通常缩写为CFSG）是完备的。因此，是时候尝试对所有（非阿贝尔）？在一卷中有两个简单组。为了说明的目的，它是方便地分为四种基本类型，即交替，经典，例外和零星组。对交替群体的研究很快发展为对应群体理论，这一理论得到了Wielandt[170]的经典文本、Dixon和Mortimer[53]的全面介绍等更现代的处理方法以及Cameron[53]等更专业的文本的很好的支持。
Thisbookisintendedasanintroductiontoallthe? nitesimplegroups. During themonumentalstruggletoclassifythe? nitesimplegroups (andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi? cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian)? nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per-tation groups, which is well served by the classic text of Wielandt [170] and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].