Topics in combinatorial group theory

Topics in combinatorial group theory [electronic resource] / Gilbert Baumslag.

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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,...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Baumslag, Gilbert
Format: Electronic eBook
Language:English
Published: Basel ; Boston : Birkhäuser, 1993.
Series:Lectures in mathematics ETH Zürich.
Subjects:
Combinatorial group theory.
Table of Contents:
  • I History
  • 1. Introduction
  • 2. The beginnings
  • 3. Finitely presented groups
  • 4. More history
  • 5. Higman's marvellous theorem
  • 6. Varieties of groups
  • 7. Small Cancellation Theory
  • II The Weak Burnside Problem
  • 1. Introduction
  • 2. The Grigorchuk-Gupta-Sidki groups
  • 3. An application to associative algebras
  • III Free groups, the calculus of presentations and the method of Reidemeister and Schreier
  • 1. Frobenius' representation
  • 2. Semidirect products
  • 3. Subgroups of free groups are free
  • 4. The calculus of presentations
  • 5. The calculus of presentations (continued)
  • 6. The Reidemeister-Schreier method
  • 7. Generalized free products
  • IV Recursively presented groups, word problems and some applications of the Reidemeister-Schreier method
  • 1. Recursively presented groups
  • 2. Some word problems
  • 3. Groups with free subgroups
  • V Affine algebraic sets and the representative theory of finitely generated groups
  • 1. Background
  • 2. Some basic algebraic geometry
  • 3. More basic algebraic geometry
  • 4. Useful notions from topology
  • 5. Morphisms
  • 6. Dimension
  • 7. Representations of the free group of rank two in SL(2,C)
  • 8. Affine algebraic sets of characters
  • VI Generalized free products and HNN extensions
  • 1. Applications
  • 2. Back to basics
  • 3. More applicatone
  • 4. Some word, conjugacy and isomorphism problems
  • VII Groups acting on trees
  • 1. Basic definitions
  • 2. Covering space theory
  • 3. Graphs of groups
  • 4. Trees
  • 5. The fundamental group of a graph of groups
  • 6. The fundamental group of a graph of groups (continued)
  • 7. Group actions and graphs of groups
  • 8. Universal covers
  • 9. The proof of Theorem 2
  • 10. Some consequences of Theorem 2 and 3
  • 11. The tree of SL2.

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