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On Systems of Equations over Free Partially Commutative Groups
Montserrat Casals-Ruiz and Ilya Kazachkov, McGill University, Montreal, QC, Canada
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Memoirs of the American Mathematical Society
2011; 153 pp; softcover
Volume: 212
ISBN-10: 0-8218-5258-2
ISBN-13: 978-0-8218-5258-3
List Price: US$77
Individual Members: US$46.20
Institutional Members: US$61.60
Order Code: MEMO/212/999
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Using an analogue of Makanin-Razborov diagrams, the authors give an effective description of the solution set of systems of equations over a partially commutative group (right-angled Artin group) \(\mathbb{G}\). Equivalently, they give a parametrisation of \(\mathrm{Hom}(G, \mathbb{G})\), where \(G\) is a finitely generated group.

Table of Contents

  • Introduction
  • Preliminaries
  • Reducing systems of equations over \(\mathbb{G}\) to constrained generalised equations over \(\mathbb{F}\)
  • The process: Construction of the tree \(T\)
  • Minimal solutions
  • Periodic structures
  • The finite tree \(T_0(\Omega)\) and minimal solutions
  • From the coordinate group \(\mathbb{G}_{R(\Omega^*)}\) to proper quotients: The decomposition tree \(T_{\mathrm{dec}}\) and the extension tree \(T_{\mathrm{ext}}\)
  • The solution tree \(T_{\mathrm{sol}}(\Omega)\) and the main theorem
  • Bibliography
  • Index
  • Glossary of notation
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