A Course in the Theory of Groups
A Course in the Theory of Groups
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DOI：
10.1007/978-1-4684-0128-8
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
D. Robinson
中科院分区：
文献类型：
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作者：
D. Robinson
《群论教程》是对群理论的全面介绍--有限群和无限群，交换群和非交换群。假定只有现代代数的基本知识，它向读者介绍了群论的不同分支及其主要成就。虽然强调统一的群论，这本书也提请注意连接与其他领域的代数，如环理论和同调代数。这个新版本已经在各个方面进行了更新，改进了一些证明，最后还包括了大约30个额外的练习。这本书有三个主要的补充。在章组扩展的阐述施赖尔的具体做法通过因素集之前，介绍了覆盖群。从教学的角度来看，这似乎是可取的。然后是S。托马斯的优雅证明的自同构塔定理是包括在部分完整的群体。最后一个小学反例的伯恩赛德问题，由于ND古普塔已被添加在一章的有限性。
A Course in the Theory of Groups is a comprehensive introduction to the theory of groups-finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra. This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to ND Gupta has been added in the chapter on finiteness properties.