群论导论 第4版（英文版） mobi 下载 fb2 夸克云 azw3 网盘 pdf pmlz

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 editions）, I have tried to select important and representative theoremsand to organize 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 editions 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 permutations into disjoint cycles andthe parity of permutations; only then is the idea of group introduced. This isconsistent with the history of Group Theory, for these first results on permu-tations can be found in an 1815 paper by Cauchy, whereas groups of permu-tations were not introduced until 1831 （by Galois）But even if history