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On Systems of Equations over Free Partially Commutative Groups
eBook ISBN:  9781470406165 
Product Code:  MEMO/212/999.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
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On Systems of Equations over Free Partially Commutative Groups
eBook ISBN:  9781470406165 
Product Code:  MEMO/212/999.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 212; 2011; 153 ppMSC: Primary 20;
Using an analogue of MakaninRazborov diagrams, the authors give an effective description of the solution set of systems of equations over a partially commutative group (rightangled 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


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 Book Details
 Table of Contents
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Volume: 212; 2011; 153 pp
MSC: Primary 20;
Using an analogue of MakaninRazborov diagrams, the authors give an effective description of the solution set of systems of equations over a partially commutative group (rightangled 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
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