Topics in Combinatorial Group Theory

1. Front Matter

   Pages i-vii

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2. History

   • Gilbert Baumslag

   Pages 1-16

3. The Weak Burnside Problem

   • Gilbert Baumslag

   Pages 17-28

4. Free groups, the calculus of presentations and the method of Reidemeister and Schreier

   • Gilbert Baumslag

   Pages 29-60

5. Recursively presentable groups, word problems and some applications of the Reidemeister-Schreier method

   • Gilbert Baumslag

   Pages 61-74

6. Affine algebraic sets and the representation theory of finitely generated groups

   • Gilbert Baumslag

   Pages 75-102

7. Generalized free products and HNN extensions

   • Gilbert Baumslag

   Pages 103-121

8. Groups acting on trees

   • Gilbert Baumslag

   Pages 123-161

9. Back Matter

   Pages 163-164

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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.

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

• Department of Mathematics, City College of New York, New York, USA

  Gilbert Baumslag

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