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 (items)). ...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
1 | |
4 | |
Subgroups of Free Groups | 13 |
Automorphisms of Free Groups | 21 |
Stabilizers in AutF | 43 |
Equations over Groups | 49 |
Quadratic Sets of Word | 58 |
Equations in Free Groups | 64 |
Aspherical Groups | 161 |
Coset Diagrams and Permutation Representations | 163 |
Behr Graphs | 170 |
Free Products and HNN Extensions | 174 |
HigmanNeumannNeumann Extensions and Free Products with Amalgamation | 178 |
Some Embedding Theorems | 188 |
Some Decision Problems | 192 |
OneRelator Groups | 198 |
Abstract Length Functions | 65 |
Representations of Free Groups the Fox Calculus | 67 |
Free Products with Amalgamation | 71 |
Generators and Relations 87 888 | 87 |
Finite Presentations | 89 |
Fox Calculus Relation Matrices Connections with Cohomology | 99 |
The ReidemeisterSchreier Method | 102 |
Groups with a Single Defining Relator | 104 |
Magnus Treatment of OneRelator Groups | 111 |
Geometric Methods | 114 |
Complexes | 115 |
Covering Maps | 118 |
Cayley Complexes | 122 |
Planar Caley Complexes | 124 |
FGroups Continued | 130 |
Fuchsian Complexes | 133 |
Planar Groups with Reflections | 146 |
Singular Subcomplexes | 149 |
Spherical Diagrams | 156 |
Bipolar Structures | 206 |
The Higman Embedding Theorem | 214 |
Algebraically Closed Groups | 227 |
Small Cancellation Theory | 235 |
The Small Cancellation Hypotheses | 240 |
The Basic Formulas | 242 |
Dehns Algorithm and Greendlingers Lemma | 246 |
The Conjugacy Problem | 252 |
The Word Problem | 259 |
The Conjugacy Problem | 262 |
Applications to Knot Groups | 267 |
The Theory over Free Products | 274 |
Small Cancellation Products | 280 |
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 Baumslag boundary cycle boundary label c₁ Cayley complex conjugacy problem conjugate contains cyclic groups cyclic words cyclically reduced defining relator Dehn's algorithm diagram e₁ edge element of G embedded equations F-group F₁ finite groups finite index finitely presented group follows free group free product Fuchsian 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 M₁ Magnus Neumann 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