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© 2001

Combinatorial Group Theory

  • Lyndon and Schupp coauthored one of the most important works on combinatorial group theory: The book was eagerly awaited by those interested in research in this area, and people working at the time remember the excitement of seeing the book when it first appeared and was passed round a lecture theatre at a conference

Book

Part of the Classics in Mathematics book series (volume 89)

Table of contents

  1. Front Matter
    Pages N1-xiv
  2. Roger C. Lyndon, Paul E. Schupp
    Pages 1-86
  3. Roger C. Lyndon, Paul E. Schupp
    Pages 87-113
  4. Roger C. Lyndon, Paul E. Schupp
    Pages 114-173
  5. Roger C. Lyndon, Paul E. Schupp
    Pages 174-234
  6. Roger C. Lyndon, Paul E. Schupp
    Pages 235-294
  7. Back Matter
    Pages 295-339

About this book

Introduction

From the reviews:
"This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 items). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979

Keywords

05E15 20Exx 20Fxx 20J05 YellowSale2006 combinatorial groups 5,00E+15 algebra automorphism cohomology Group theory

Authors and affiliations

  1. 1.Dept. of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Dept. of MathematicsUniversity of IllinoisUrbanaUSA

About the authors

Biography of Roger C. Lyndon

Roger Lyndon, born on Dec. 18, 1917 in Calais (Maine, USA), entered Harvard University in 1935 with the aim of studying literature and becoming a writer. However, when he discovered that, for him, mathematics required less effort than literature, he switched and graduated from Harvard in 1939.

After completing his Master's Degree in 1941, he taught at Georgia Tech, then returned to Harvard in 1942 and there taught navigation to pilots while, supervised by S. MacLane, he studied for his Ph.D., awarded in 1946 for a thesis entitled The Cohomology Theory of Group Extensions.

Influenced by Tarski, Lyndon was later to work on model theory. Accepting a position at Princeton, Ralph Fox and Reidemeister's visit in 1948 were major influencea on him to work in combinatorial group theory. In 1953 Lyndon left Princeton for a chair at the University of Michigan where he then remained except for visiting professorships at Berkeley, London, Montpellier and Amiens.

Lyndon made numerous major contributions to combinatorial group theory. These included the development of "small cancellation theory", his introduction of "aspherical" presentations of groups and his work on length functions. He died on June 8, 1988.

 

Biography of Paul E. Schupp

Paul Schupp, born on March 12, 1937 in Cleveland, Ohio was a student of  Roger Lyndon's at the Univ. of Michigan. Where he wrote a thesis on "Dehn's Algorithm and the Conjugacy Problem". After a year at the University of Wisconsin he moved to the University of Illinois where he remained. For several years he was also concurrently Visiting Professor at the University Paris VII and a member of the Laboratoire d'Informatique Théorique et Programmation (founded by M. P. Schutzenberger).

Schupp further developed the use of cancellation diagrams in combinatorial group theory, introducing conjugacy diagrams, diagrams on compact surfaces, diagrams over free products with amalgamation and HNN extensions and applications to Artin groups. He then worked with David Muller on connections between group theory and formal language theory and on the theory of finite automata on infinite inputs. His current interest is using geometric methods to investigate the computational complexity of algorithms in combinatorial group theory.

Bibliographic information

  • Book Title Combinatorial Group Theory
  • Authors Roger C. Lyndon
    Paul E. Schupp
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-61896-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-07642-1
  • Softcover ISBN 978-3-540-41158-1
  • eBook ISBN 978-3-642-61896-3
  • Series ISSN 1431-0821
  • Edition Number 1
  • Number of Pages XIV, 339
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Reprint of the 1977 Edition (Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 89)
  • Topics Group Theory and Generalizations
    Numerical Analysis
  • Buy this book on publisher's site

Reviews

From the reviews:

"This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 items). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979

"This is a reprint of the 1977 edition … of this famous and very popular book, which became a desk copy for everybody who is dealing with combinatorial group theory. The complete bibliography (more than 1000 titles) well reflects the situation in the combinatorial group theory at the time when the book was published. Definitely, since the face of combinatorial group theory has significantly changed … this well-written book still is very functional and efficient." (Igor Subbotin, Zentralblatt MATH, Vol. 997 (22), 2002)