Topics in combinatorial group theory [electronic resource] / Gilbert Baumslag.
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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Full Text (via Springer) |
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Main Author: | |
Format: | Electronic eBook |
Language: | English |
Published: |
Basel ; Boston :
Birkhäuser,
1993.
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Series: | Lectures in mathematics ETH Zürich.
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Subjects: |
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.