Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

by Wilhelm Magnus, Abraham Karrass, Donald Solitar

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.

Genres: Mathematics

464 pages, Paperback

First published January 1, 1966

Reviews

[Michael · Rating 2 out of 5]

Disjointed - like journal papers by different authors stapled together.

Chapter 5 is especially bad spending 100 pages developing the idea of free algebras for one proof without any real motivation or connection to the rest of the book.