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Medientyp:
E-Book
Titel:
Combinatorial Group Theory
Enthält:
I. Free Groups and Their Subgroups1. 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 -- 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 -- 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 -- 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 -- 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 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 -- Russian Names in Cyrillic -- Index of Names.
Reproduktionsreihe:
Springer eBook Collection. Mathematics and Statistics
Entstehung:
Anmerkungen:
Beschreibung:
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