组合群论
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作者Roger C. Lyndon，Paul E. Schupp著
出版社世界图书出版公司北京公司
ISBN9787519202576
出版时间2016-03
装帧平装
开本16开
定价55元
货号8745811
上书时间2024-09-10
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作者简介
Roger Lyndon, born on Dec.18,1917 in Calais (Maine, USA), entered Harvard University in 1935 with the aim ofstudying literature and becoming awriter. However, when he discoveredthat, for him, mathematics requiredless effort than literature, he switchedand graduated from Harvard in 1939.After completing his Master s Degreein 1941, he taught at Georgia Tech,then returned to Harvard in1942 and there taught navigation topilots while, supervised by S. MacLane, he studied for his Ph.D.,awarded in 1946 for a thesis entitled The Cohomology Theory ofGroup Extensions.Influenced by Tarski, Lyndon was later to work on model theory.Accepting a position at Princeton, Ralph Fox and Reidemeister svisit in 1948 were major influencea on him to work in combinat-orial group theory, in 1953 Lyndon left Princeton for a chair at theUniversity of Michigan where he then remained except for visitingprofessorships at Berkeley, London, Montpellier and Amiens.Lyndon made numerous major contributions to combinatorialgroup theory. These included the development of "small cancellationtheory", his introduction of"aspherical" presentations of groupsand his work on length functions. He died on June 8, 1988.
目录
Chapter Ⅰ．Free Groups and Their SubgroupsI．Introduction2．Nielsens Method3．Subgroups of Free Groups4．Automorphisms of Free Groups5．Stabilizers in Aut（F）6．Equations over Groups7．Quadratic Sets of Word8．Equations in Free Groups9．Abstract Length Functions10．Representations of Free Groups； the Fox Calculus11．Free Products with AmalgamationChapler Ⅱ．Generators and RelationsI．Introduction2．Finite Presentations3．Fox Calculus， Relation Matrices， Connections with Cohomology4．The Reidemeister-Schreier Method5．Groups with a Single Defining Relator6．Magnus Treatment of One-Relator GroupsChapter Ⅲ．Geometric Methods1．Introduction2．Complexes3．Covering Maps4．Cayley Complexes5．Planar Caley Complexes6．F-Groups Continued7．Fuchsian Complexes8．Planar Groups with Reflections9．Singular Subcomplexes10．Spherical Diagrams11．Aspherical Groups12．Coset Diagrams and Permutation Representations13．Behr GraphsChapter Ⅳ．Free Products and HNN Extensions1．Free Products2．Higman-Neumann-Neumann Extensions and Free Products with Amalgamation3．Some Embedding Theorems4．Some Decision Problems5．One-Relator Groups6．Bipolar Structures7．The Higman Embcdding Theorem8．Algebraically Closed GroupsChapter Ⅴ．Small Cancellation Theory1．Diagrams2．The Small Cancellation Hypotheses3．The Basic Formulas4．Dehns Algorithm and Greendtingers Lemma5．The Conjugacy Problem6．The Word Problem7．The Conjugacy Problem8．Applications to Knot Groups9．The Theory over Free Products10．Small Cancellation Products11．Small Cancellation Theory over Free Products with Amalgamation and HNN ExtensionsBibliographyRussian Names in CyrillicIndex of NamesSubject Index
内容摘要
林登所著的《组合群论（英文版）》对组合群论作了范畴界定。将对该领域的研究浓缩在这339页书里，真是一个相当可观的科研成果。书中包括大量有用的参考书目（超过1100本）。该书对这些文献作了有益的且受欢迎的补充，包括许多在别的书中没有的科研成果。该书无疑是一本标准的参考书。
精彩内容
该书对组合群论作了范畴界定。将对该领域的研究浓缩在这339页书里，真是一个相当可观的科研成果。书中包括大量有用的参考书目（超过1100本）。该书对这些文献作了有益的且受欢迎的补充，包括许多在别的书中没有的科研成果。该书无疑是一本标准的参考书。
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