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Combinatorial Group Theory
Edited by: Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang
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Contemporary Mathematics
1990; 191 pp; softcover
Volume: 109
ISBN-10: 0-8218-5116-0
ISBN-13: 978-0-8218-5116-6
List Price: US$46
Member Price: US$36.80
Order Code: CONM/109
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The AMS Special Session on Combinatorial Group Theory--Infinite Groups, held at the University of Maryland in April 1988, was designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results. The session reflected the vitality and interests in infinite group theory, with eighteen speakers presenting lectures covering a wide range of group-theoretic topics, from purely logical questions to geometric methods. The heightened interest in classical combinatorial group theory was reflected in the sheer volume of work presented during the session.

This book consists of eighteen papers presented during the session. Comprising a mix of pure research and exposition, the papers should be sufficiently understandable to the nonspecialist to convey a sense of the direction of this field. However, the volume will be of special interest to researchers in infinite group theory and combinatorial group theory, as well as to those interested in low-dimensional (especially three-manifold) topology.

Table of Contents

  • G. Baumslag -- Some reflections on finitely generated metabelian groups
  • B. Fine and G. Rosenberger -- Conjugacy separability of Fuchsian groups and related questions
  • B. Fine, F. Rohl, and G. Rosenberger -- Two-generator subgroups of certain HNN groups
  • T. Fournelle and K. Weston -- A geometric approach to some group presentations
  • A. Gaglione and D. Spellman -- \(\gamma_n+1(F)\) and \(F/\gamma_n+1(F)\) revisited
  • A. Gaglione and H. Waldinger -- The commutator collection process
  • L. Kappe and R. Morse -- Levi-properties in metabelian groups
  • K. Kuiken and J. Masterson -- Monodromy groups of differential equations on Riemann surfaces of genus \(1\)
  • J. Labute -- The Lie algebra associated to the lower central series of a free product of cyclic groups of prime order \(p\)
  • J. Levine -- Algebraic closure of groups
  • A. Macbeath -- Automorphisms of Riemann surfaces
  • I. Macdonald and B. H. Neumann -- On commutator laws in groups, \(2\)
  • J. McCool -- Two-dimensional linear characters and automorphisms of free groups
  • J. Ratcliffe -- On the uniqueness of amalgamated product decompositions of a group
  • L. Ribes -- The Cartesian subgroup of a free product of profinite groups
  • D. Robinson -- A note on local coboundaries for locally nilpotent groups
  • C. Y. Tang -- Some results on \(1\)-relator quotients of free products
  • M. Tretkoff -- Covering spaces, subgroup separability, and the generalized M. Hall property
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