Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
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 
Click above image for expanded view
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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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
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
Please select which format for which you are requesting permissions.