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Mathematics - Algebra | Combinatorial Group Theory

Combinatorial Group Theory

Lyndon, Roger C., Schupp, Paul E.

Originally published as volume 89 in the series: Ergebnisse der Mathematik und ihrer Grenzgebiete

Softcover reprint of the original 1st ed. 2001, XIV, 339 p.


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From the reviews:
"This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 ÄitemsÜ). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979

Content Level » Research

Keywords » 05E15 - 20Exx - 20Fxx - 20J05 - YellowSale2006 - combinatorial groups

Related subjects » Algebra - Computational Science & Engineering

Table of contents 

Chapter I. Free Groups and Their Subgroups 1. 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 Lenght Functions 10. Representations of Free Groups 11. Free Pruducts with Amalgamation Chapter II. Generators and Relations 1. 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. Sherical Diagrams 11. Aspherical Groups 12. Coset Diagrams and Permutation Representations 13. Behr Graphs Chpter 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 Embedding 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 Greendlinger's Lemma 5. The Conjugacy Problem 6. The Word Problem 7. The Cunjugacy Problme 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 Index of Names Subject Index

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