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On Systems of Equations over Free Partially Commutative Groups
 
Montserrat Casals-Ruiz McGill University, Montreal, QC, Canada
Ilya Kazachkov McGill University, Montreal, QC, Canada
On Systems of Equations over Free Partially Commutative Groups
eBook ISBN:  978-1-4704-0616-5
Product Code:  MEMO/212/999.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
On Systems of Equations over Free Partially Commutative Groups
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On Systems of Equations over Free Partially Commutative Groups
Montserrat Casals-Ruiz McGill University, Montreal, QC, Canada
Ilya Kazachkov McGill University, Montreal, QC, Canada
eBook ISBN:  978-1-4704-0616-5
Product Code:  MEMO/212/999.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2122011; 153 pp
    MSC: Primary 20;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Reducing systems of equations over $\mathbb {G}$ to constrained generalised equations over $\mathbb {F}$
    • 4. The process: construction of the tree $T$
    • 5. Minimal solutions
    • 6. Periodic structures
    • 7. The finite tree $T_0(\Omega )$ and minimal solutions
    • 8. From the coordinate group $\mathbb {G}_{R(\Omega ^*)}$ to proper quotients: the decomposition tree $T_{\mathrm {dec}}$ and the extension tree $T_{\mathrm {ext}}$
    • 9. The solution tree $T_{sol}(\Omega )$ and the main theorem
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2122011; 153 pp
MSC: Primary 20;

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.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Reducing systems of equations over $\mathbb {G}$ to constrained generalised equations over $\mathbb {F}$
  • 4. The process: construction of the tree $T$
  • 5. Minimal solutions
  • 6. Periodic structures
  • 7. The finite tree $T_0(\Omega )$ and minimal solutions
  • 8. From the coordinate group $\mathbb {G}_{R(\Omega ^*)}$ to proper quotients: the decomposition tree $T_{\mathrm {dec}}$ and the extension tree $T_{\mathrm {ext}}$
  • 9. The solution tree $T_{sol}(\Omega )$ and the main theorem
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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