Combinatorial group theory

Title page
Prefaces
Technical Remarks
Chapter 1 Basic Concepts
	1.1 Introduction
	1.2 Construction of groups from generators and defining relators
	1.3 Dehn\'s fundamental problems
	1.4 Definition and elementary properties of free groups
	1.5 Tietze transformations
	1.6 Graph of a group
Chapter 2 Factor Groups and Subgroups
	2.1 Factor groups
	2.2 Verbal subgroups and reduced free groups
	2.3 Presentations of subgroups (The Reidemeister-Schreier method)
	2.4 Subgroups of free groups
Chapter 3 Nielsen Transformations
	3.1 Introduction
	3.2 A reduction process
	3.3 The commutator quotient group
	3.4 A test for isomorphism
	3.5 The automorphism group  n of free groups
	3.6 Free automorphisms and free isomorphisms
	3.7 Braid groups and mapping class groups
Chapter 4 Free Products and Free Products with Amalgamations
	4.1 Pree products
	4.2 Pree product with amalgamated subgroups
	4.3 Subgroup theorems for free and amalgamated products
	4.4 Groups with one defining relator
Chapter 5 Commutator Calculus
	5.1 Introduction
	5.2 Commutator identities
	5.3 The lower central series
	5.4 Some freely generated graded algebras
	5.5 A mapping of a free group into A(Z, r)
	5.6 Lie elements and basis theorems
	5.7 The lower central series of free groups
	5.8 Some applications
	5.9 Identities
	5.10 The Baker-Hausdorff formula
	5.11 Power relations and commutator relations
	5.12 Burnside\'s problem, Exponents 3 and 4
	5.13 Burnside\'s problem, Report on e > 4
	5.14 Topological aspects
	5.15 Free differential calculus
Chapter 6 Introduction to Some Recent Developments
	6.1 Word, conjugacy, and related problems
	6.2 Adjunction and embedding problems
	6.3 Varieties of groups
	6.4 Products of groups
	6.5 Residual and Hopfian properties
References
List of Theorems, Corollaries, and Definitions
List of Symbols and Abbreviations
Index