# Combinatorial Group Theory

@inproceedings{Lyndon1977CombinatorialGT, title={Combinatorial Group Theory}, author={Roger Lyndon and Paul E. Schupp}, year={1977} }

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…

## 2,137 Citations

### Rings of Fricke characters and automorphism groups of free groups

- Mathematics
- 1980

Let F n be the free group on n free generators g~(v= 1, ..., n) and let ~ , be its group of automorphisms. Its quotient group (b* with respect to the inner automorphisms is the group of automorphism…

### Extensions of free groups: algebraic, geometric, and algorithmic aspects

- Mathematics
- 2017

In this work we use geometric techniques in order to study certain natural extensions of free groups, and solve several algorithmic problems on them.
To this end, we consider the family of…

### 2 Free Groups : Definitions and Basic Theorems

- Mathematics
- 2014

Combinatorial Group theory is the study of free groups and group presentations. Group presentations are a representation of a group as a set of relations on a generating set. Combinatorial group…

### SOME APPLICATIONS OF ALGEBRAIC TOPOLOGICAL METHODS TO GROUP THEORY

- Mathematics
- 2007

In this talk, using properties of fundamental groups and covering spaces of connected polyhedra, we present topological proof for some famous theorems in group theory such as Nielsen-Schreier…

### On graphs representing automorphisms of free groups

- Mathematics
- 1989

For every automorphism f of the free group F = (xl, ... ,, -) Gersten [2, Theorem 5.6] constructed a finite graph representing f and used this graph to give the first proof of Scott's conjecture that…

### Free Groups, Their Automorphism Groups, Applications

- Mathematics
- 1993

The free group F n with n generators and its automorphism group Φ n , studied in combinatorial group theory, provide an algebraic non-commutative scheme for quasiperiodic systems. Homomorphisms from…

### On linear and residual properties of graph products.

- Mathematics
- 1999

Graph groups are groups with presentations where the only relators are commutators of the generators. Graph groups were first investigated by Baudisch [1], and much subsequent foundational work was…

### The indices of torsion-free subgroups of Fuchsian groups

- Mathematics
- 1983

Elementary algebraic techniques are used to obtain the precise possible indices of torsion-free subgroups of finite index of finitely generated Fuchsian groups (and related groups). Introduction. In…

### J un 2 00 8 Embeddings and chains of free groups

- Mathematics
- 2008

We build a nonabelian CSA-group in which maximal abelian subgroups are conjugate and divisible and in which quantifier-free definable sets are stable. For n ≥ 1, let Fn denote the free group on n…