Using an analogue of Makanin-Razborov diagrams, we give a description of the solution set of systems of equations over an equationally Noetherian free product of groups $G$. Equivalently, we give a parametrisation of the set $\Hom(H, G)$ of all homomorphisms from a finitely generated group $H$ to $G$. Furthermore, we show that every algebraic set over $G$ can be decomposed as a union of finitely many images of algebraic sets of NTQ systems. If the universal Horn theory of $G$ (the theory of quasi-identities) is decidable, then our constructions are effective. / Utilisant un analogue des diagrammes de Makanin-Razborov, nous donnons une description de l'ensemble des solutions de systémes d'équations dans un produit libre équationallement Noetherien $G$. De maniére équivalente, nous donnons une paramétrisation de l'ensemble $\Hom(H,G)$ des homomorphismes d'un groupe de génération finie $H$à $G$.Si la théorie universelle de Horn de $G$ est décidable, nos constructions sont algorithmique.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.66911 |
| Date | January 2009 |
| Creators | Kazachkov, Ilya |
| Contributors | Alexei Miasnikov (Internal/Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics and Statistics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | Electronically-submitted theses. |
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