群论导论 第4版（英文版） 阿里云 lit azw3 txt pdf caj 下载 在线

本版传承了前几版之表述清晰的风格，并在此基础上对内容进行了全面修正与改编。开篇介绍了群与同态的基本性质，涵盖的主题包括Lagrange定理、Noether同构定理、对称群、G-集、Sylow定理，有限Abel群、Krull-Schmidt定理、可解及幂零群，Jordan-Holder定理。随后中间几章应用Jordan-Holder定理组织了关于扩张（同构群、半直积、Schur-Zassenhaus引理，Schur乘子）及单群（射影幺模群的简单性，以及回到G-集的讨论后，构造零散Mathieu群）的讨论。本书*后三章的内容有：无限Abel群（重点讨论可数群）；自由群及群表示、陪集枚举、自由积、共合及HNN扩张；以及有限表示群问题，和Higman嵌入定理与群同构问题的不可判定性的完全性证明。目次：群与同态；构定理；对称群与G集；Sylow定理； 正合列；有限直积；扩张与上同调；一些单线性群；置换与Mathieu群；Abel群；自由群与自由积；字问题。

读者对象：本书适用于学习过抽象代数与线性代数的本科生与研究生。

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Joseph J. Rotman，美国伊利诺伊大学（University of Illinois）数学系教授，An Introduction to the Theory of Groups，An Introduction to Homological Algebra，An Introduction to Algebraic Topology 这三部著作均被世图引进出版。

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书籍介绍

《群论导论(第4版)(英文版)》介绍了：Group Theory is a vast subject and, in this Introduction （as well as in theearlier editi***）, I have tried to select important and representative theoremsand to ***anize them in a coherent way. Proofs must be clear, and examplesshould illustrate theorems and also explain the presence of restrictive hypo-theses. ！ also believe that some history should be given so that one canunderstand the origin of problems and the context in which the subjectdeveloped. Just as each of the earlier editi*** differs from the previous one in a signifi-cant way, the present （fourth） edition is genuinely different from the third.Indeed, this is already apparent in the Table of Contents. The book nowbegins with the unique factorization of permutati*** into disjoint cycles andthe parity of permutati***; only then is the idea of group introduced. This isc***istent with the history of Group Theory, for these first results on permu-tati*** can be found in an 1815 paper by Cauchy, whereas groups of permu-tati*** were not introduced until 1831 （by Galois）But even if history