作者介紹
(美)林登
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.
目錄
Chapter Ⅰ.Free Groups and Their Subgroups
I.Introduction
2.Nielsen's Method
3.Subgroups of Free Groups
4.Automorphisms of Free Groups
5.Stabilizers in Aut（F）
6.Equations over Groups
7.Quadratic Sets of Word
8.Equations in Free Groups
9.Abstract Length Functions
10.Representations of Free Groups； the Fox Calculus
11.Free Products with Amalgamation
Chapler Ⅱ.Generators and Relations
I.Introduction
2.Finite Presentations
3.Fox Calculus， Relation Matrices， Connections with Cohomology
4.The Reidemeister-Schreier Method
5.Groups with a Single Defining Relator
6.Magnus' Treatment of One-Relator Groups
Chapter Ⅲ.Geometric Methods
1.Introduction
2.Complexes
3.Covering Maps
4.Cayley Complexes
5.Planar Caley Complexes
6.F-Groups Continued
7.Fuchsian Complexes
8.Planar Groups with Reflections
9.Singular Subcomplexes
10.Spherical Diagrams
11.Aspherical Groups
12.Coset Diagrams and Permutation Representations
13.Behr Graphs
Chapter Ⅳ.Free Products and HNN Extensions
1.Free Products
2.Higman-Neumann-Neumann Extensions and Free Products with Amalgamation
3.Some Embedding Theorems
4.Some Decision Problems
5.One-Relator Groups
6.Bipolar Structures
7.The Higman Embcdding Theorem
8.Algebraically Closed Groups
Chapter Ⅴ.Small Cancellation Theory
1.Diagrams
2.The Small Cancellation Hypotheses
3.The Basic Formulas
4.Dehn's Algorithm and Greendtinger's Lemma
5.The Conjugacy Problem
6.The Word Problem
7.The Conjugacy Problem
8.Applications to Knot Groups
9.The Theory over Free Products
10.Small Cancellation Products
11.Small Cancellation Theory over Free Products with Amalgamation and HNN Extensions
Bibliography
Russian Names in Cyrillic
Index of Names
Subject Index
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