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

Wilhelm Magnus (Author), Abraham Karrass (Author), Donald Solitar (Author)

Book Description

Publication Date: November 12, 2004 | Series: 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.

Product Details

• Paperback: 464 pages
• Publisher: Dover Publications; 2 Revised edition (November 12, 2004)
• Language: English
• ISBN-10: 0486438309
• ISBN-13: 978-0486438306
• Product Dimensions: 8.4 x 5.5 x 0.9 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #553,591 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 2 people found the following review helpful:

3.0 out of 5 stars At least I know what's in this book now, July 10, 2011

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Scott (Dubuque, IA) - See all my reviews

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This review is from: Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations (Dover Books on Mathematics) (Paperback)

In 2010, while doverpublications.com was running huge markdowns on a lot of technical books and I ordered a bunch of those sale books, this 'Combinatorial Group Theory' text looked possibly interesting, but was at a pricey $27.95 and never went on sale. I have long been interested in combinatorics and discrete math, and have read significantly in those fields, so what is 'combinatorial' group theory anyway? Finally in May 2011, at a 34% markdown to $18.45, I got the book from Amazon.

This text does look like an interestingly different form of group theory, though it's near to graduate level and is plagued by a fairly frequent problem with Dover books, a very small font size, with hyper small subscripts and superscripts, which are plentiful. Most likely, this tiny font resulted from the 1966 original book on Wiley Interscience having a much larger page size than the 5.375"x8.5" most common Dover page size, so the pages were shrunken markedly to make the Dover reprint.

In a couple of other combinatorial group theory documents I either have (lecture note PDFs), or have examined in Amazon, this book by Magnus, Karrass and Solitar is one of the most ground-breaking reference treatments of the subject.

I did transfer this difficult book with its tiny font to cardboard box storage from my bookshelves on Sat 17Dec11, to make room for other more viable books on the shelf where this was.

CONTENTS: Technical Remarks / 1 Basic Concepts / 2 Factor Groups and Subgroups / 3 Nielsen Transformations / 4 Free Products and Free Products with Amalgamations / 5 Commutator Calculus / 6 Introduction to Some Recent Developments / References / List of Theorems, Corollaries, and Definitions / List of Symbols and Abbreviations / Index / 464 pages