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Exponential Genus Problems in One-Relator Products of Groups
A. J. Duncan, University of Newcastle, Newcastle upon Tyne, England

Memoirs of the American Mathematical Society
2007; 156 pp; softcover
Volume: 186
ISBN-10: 0-8218-3945-4
ISBN-13: 978-0-8218-3945-4
List Price: US$72
Individual Members: US$43.20
Institutional Members: US$57.60
Order Code: MEMO/186/873
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Exponential equations in free groups were studied initially by Lyndon and Schützenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.

Table of Contents

  • Introduction
  • Quadratic words
  • Quadratic exponential equations and \({\mathcal L}\)-genus
  • Resolutions of quadratic equations
  • Decision problems
  • Pictures
  • Corridors
  • Angle assignment
  • Curvature
  • Configurations \(C\)
  • Configurations \(D\)
  • Final angle adjustment
  • Isoperimetry
  • Proof of Theorem 5.9
  • Bibliography
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