CMS Books in Mathematics

Combinatorial Methods

Free Groups, Polynomials, and Free Algebras

Authors: Shpilrain, Vladimir, Mikhalev, Alexander, Yu, Jie-tai

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eBook 89,24 €
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  • ISBN 978-0-387-21724-6
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover 109,19 €
price for Spain (gross)
  • ISBN 978-0-387-40562-9
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 109,19 €
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  • ISBN 978-1-4419-2344-8
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

 The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).

Reviews

From the reviews:

"This book is devoted to a combinatorial theory of three types of objects: (1) free groups, (2) polynomial algebras and free associative algebras, (3) free algebras of the so-called Nielsen-Schreier varieties of algebras. It considers problems related mainly to the groups of automorphisms of these objects... The authors have done a lot of work to show that the same problems and the same ideas are the moving forces of the three theories. The book contains a good background on the classical results (most of them without proof) and a detailed exposition of the recent results. A large portion of the exposition is devoted to topics in which the authors have made their own contribution." -- MATHEMATICAL REVIEWS

"The book consists of three parts: groups, polynomial algebras and free Nielsen-Schreier algebras. … The book contains very interesting material to which the authors have made a valuable contribution. The book includes many open and very important problems. … The exposition of the material is made with care. So the book could be recommended for students even as a textbook." (Vyacheslav A. Artamonov, Zentralblatt MATH, Vol. 1039 (8), 2004)


Table of contents (15 chapters)

  • Introduction

    Mikhalev, Alexander A. (et al.)

    Pages 1-3

    Preview Buy Chapter 30,19 €
  • Classical Techniques of Combinatorial Group Theory

    Mikhalev, Alexander A. (et al.)

    Pages 9-19

    Preview Buy Chapter 30,19 €
  • Test Elements

    Mikhalev, Alexander A. (et al.)

    Pages 20-34

    Preview Buy Chapter 30,19 €
  • Other Special Elements

    Mikhalev, Alexander A. (et al.)

    Pages 35-44

    Preview Buy Chapter 30,19 €
  • Automorphic Orbits

    Mikhalev, Alexander A. (et al.)

    Pages 45-64

    Preview Buy Chapter 30,19 €

Buy this book

eBook 89,24 €
price for Spain (gross)
  • ISBN 978-0-387-21724-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 109,19 €
price for Spain (gross)
  • ISBN 978-0-387-40562-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 109,19 €
price for Spain (gross)
  • ISBN 978-1-4419-2344-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Methods
Book Subtitle
Free Groups, Polynomials, and Free Algebras
Authors
Series Title
CMS Books in Mathematics
Copyright
2004
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-21724-6
DOI
10.1007/978-0-387-21724-6
Hardcover ISBN
978-0-387-40562-9
Softcover ISBN
978-1-4419-2344-8
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XII, 315
Topics