Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations (Dover Books on Mathematics)

This seminal, much-cited account 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 commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition. A seminal, much-cited account of combinatorial group theory coauthored 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 commutator 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.

This classic graduate text builds from the basics of combinational group theory in the construction of groups from generators and defining relators, to Dehn's fundamental problem, definition and elementary properties of free groups, and Tietze transformations. It then describes factor groups and subgroups (the Reidemeister-Schreier method), Nielsen transformations, free products and free products with amalgamations, commutator calculus, and some recent developments in the field. The authors supply lists of theorems, corollaries definitions, symbols and abbreviations. This is a reprint of the 1976 edition originally published by Interscience Publishers. Annotation ©2004 Book News, Inc., Portland, OR