Combinatorial group theory.
type: Item
instance of: scholarly article
title: Combinatorial group theory.
zbMATH Open document ID: 0997.20037
author: Roger C. Lyndon
author: Paul E. Schupp
published in: Classics in Mathematics
publication date: 2001-01-17T00:00:00Z
review text: This is a reprint of the 1977 edition (Zbl 0368.20023) of this famous and very popular book, which became a desk copy for everybody who is dealing with combinatorial group theory. The authors describe with details two broad methods. The first part of the book (free groups and their subgroups, and generators and relations) is dedicated to the fundamental algorithms of Nielsen, Reidemeister, Schreier, Tietze and Whitehead. The authors prove the Freiheitssatz in different ways in order to show the power of fundamental methods. The second part is about geometric methods, free products and HNN extensions, and small cancellation 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 the combinatorial group theory has significantly changed (for instance, by works of A. Yu. Ol'shanskij and his students), this well-written book still is very functional and efficient.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F06
Mathematics Subject Classification ID: 20F10
zbMATH DE Number: 1554175
zbMATH Keywords: free groups
zbMATH Keywords: subgroups
zbMATH Keywords: generators
zbMATH Keywords: relations
zbMATH Keywords: Freiheitssatz
zbMATH Keywords: free products
zbMATH Keywords: HNN extensions
zbMATH Keywords: small cancellation theory
reviewed by: Igor Subbotin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1554175