Combinatorial Group TheoryFrom 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 |
Contents
Chapter I Free Groups and Their Subgroups | 1 |
2 Nielsens Method | 4 |
3 Subgroups of Free Groups | 13 |
4 Automorphisms of Free Groups | 21 |
5 Stabilizersin AutF | 43 |
6 Equations over Groups | 49 |
7 Quadratic Sets of Word | 58 |
8 Equations in Free Groups | 64 |
11 Aspherical Groups | 161 |
12 Coset Diagrams and Permutation Representations | 163 |
13 Behr Graphs | 170 |
Chapter IV Free Products and HNN Extensions | 174 |
2 HigmanNeumannNeumann Extensions and Free Products with Amalgmation | 178 |
3 Some Embedding Theorems | 188 |
4 Some Decision Problems | 192 |
5 OneRelator Groups | 198 |
9 Abstract Length Functions | 65 |
10 Representations of Free Groups the Fox Calculus | 67 |
11 Free Products with Amalgamation | 71 |
Chapter II Generators and Relations | 87 |
2 Finite Presentations | 89 |
3 Fox Calculus Relation Matrices Connections with Cohomology | 99 |
4 The ReidemeisterSchreier Method | 102 |
5 Groups with a Single Defining Relator | 104 |
6 Magnus Treatment of OneRelator Groups | 111 |
Chapter III Geometric Methods | 114 |
2 Complexes | 115 |
3 Covering Maps | 118 |
4 Cayley Complexes | 122 |
5 Planar Cayley Complexes | 124 |
6 FGroups Continued | 130 |
7 Fuchsian Complexes | 133 |
8 Planar Groups with Reflections | 146 |
9 Singular Subcomplexes | 149 |
10 Spherical Diagrams | 156 |
6 Bipolar Structures | 206 |
7 The Higman Embedding Theorem | 214 |
8 Algebraically Closed Groups | 227 |
Chapter V Small Cancellation Theory | 235 |
2 The Small Cancellation Hypotheses | 240 |
3 The Basic Formulas | 242 |
4 Dehas Algorithm and Greendlingefs Lemma | 246 |
5 The Conjugacy Problem | 252 |
6 The Word Problem | 259 |
7 The Conjugacy Problem | 262 |
8 Applications to Knot Groups | 267 |
9 The Theory over Free Products | 274 |
10 Small Cancellation Products | 280 |
11 Small Cancellation Theory Over Free Products with Amalgamation and HNN Extensions | 285 |
Bibliography | 295 |
Russian Names in Cyrillic | 332 |
| 333 | |
| 336 | |
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Common terms and phrases
a₁ abelian Algebra algebraically closed group algorithm Amer Aut(F automorphism b₁ Baumslag boundary cycle boundary label c₁ Cayley complex conjugacy problem conjugate contains cyclic groups cyclic words cyclically reduced defining relator Dehn's algorithm diagram edge element of G embedded equations F-group F₁ finite groups finite index finitely presented group follows free group free product Fuchsian groups fundamental group G₁ G₂ group G h₁ hence Higman HNN extension homomorphism hypothesis implies induction infinite isomorphic Karrass Lemma length Let F Let G London Math loop Lyndon Magnus Neumann non-trivial element normal closure normal form normal subgroup obtained one-relator groups p₁ permutation presentation G Proc product with amalgamation proof Proposition quotient group r₁ r₂ rank region residually finite groups result S₁ satisfies sequence small cancellation Solitar subgroup of G subset suppose t₁ theorem theory trivial u₁ v₁ vertex vertices w₁ whence X₁ y₁ Zieschang