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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 |
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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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 212; 2011; 153 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Reducing systems of equations over $\mathbb {G}$ to constrained generalised equations over $\mathbb {F}$
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4. The process: construction of the tree $T$
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5. Minimal solutions
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6. Periodic structures
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7. The finite tree $T_0(\Omega )$ and minimal solutions
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8. From the coordinate group $\mathbb {G}_{R(\Omega ^*)}$ to proper quotients: the decomposition tree $T_{\mathrm {dec}}$ and the extension tree $T_{\mathrm {ext}}$
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9. The solution tree $T_{sol}(\Omega )$ and the main theorem
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Volume: 212; 2011; 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
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