Combinatorial group theory 组合群伦

A seminal, much-cited account of combinatorial group theory—co-authored by a distinguished teacher of mathematics and a pair of his colleagues--this text for graduate students features numerous helpful exercises.
　　The book begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commentator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; varieties of groups; products of groups; and residual and Hopfian properties.
　　In addition to the exercises, which appear throughout the text, supplementary materials include an extensive bibliography of important books and monographs, as well as a list of theorems, corollaries, and definitions and a list of symbols and abbreviations.

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　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　Free products
　4.2　Free 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-Hausdorffformula
　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