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Topics in Combinatorial Group Theory

  • Gilbert Baumslag

Part of the Lectures in Mathematics ETH Zürich book series (LM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Gilbert Baumslag
    Pages 1-16
  3. Gilbert Baumslag
    Pages 17-28
  4. Gilbert Baumslag
    Pages 103-121
  5. Gilbert Baumslag
    Pages 123-161
  6. Back Matter
    Pages 163-164

About this book

Introduction

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

Keywords

Algebra Finite Fundamental group Graph Group theory Morphism Topology algorithms calculus equation function geometry proof theorem

Authors and affiliations

  • Gilbert Baumslag
    • 1
  1. 1.Department of MathematicsCity College of New YorkNew YorkUSA

Bibliographic information