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Essays in Group Theory

  • Book
  • © 1987
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Overview

Editors:
  1. S. M. Gersten

    1. Department of Mathematics, University of Utah, Salt Lake City, USA

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Part of the book series: Mathematical Sciences Research Institute Publications (MSRI, volume 8)

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Table of contents (5 chapters)

  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
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  3. Reducible Diagrams and Equations Over Groups

    • S. M. Gersten
    Pages 15-73
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  4. Hyperbolic Groups

    • M. Gromov
    Pages 75-263
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  5. Dendrology of Groups: An Introduction

    • Peter B. Shalen
    Pages 265-319
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  6. Adian Groups and Pregroups

    • John R. Stallings
    Pages 321-342
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About this book

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.

Editors and Affiliations

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

    S. M. Gersten

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