Essays in Group Theory

1. Front Matter

   Pages i-vii

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2. Affine Algebraic Sets and Some Infinite Finitely Presented Groups

   • Gilbert Baumslag, Peter B. Shalen

   Pages 1-14

3. Reducible Diagrams and Equations Over Groups

   • S. M. Gersten

   Pages 15-73

4. Hyperbolic Groups

   • M. Gromov

   Pages 75-263

5. Dendrology of Groups: An Introduction

   • Peter B. Shalen

   Pages 265-319

6. Adian Groups and Pregroups

   • John R. Stallings

   Pages 321-342

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.

• Group theory
• algebra
• group action
• representation theory

• Department of Mathematics, University of Utah, Salt Lake City, USA

  S. M. Gersten

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