On Systems of Equations over Free Products of Groups

Abstract

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.

71 pages, 13 figures

References in corpus (3)

• Unification theorems in algebraic geometry
• On Systems of Equations over Free Partially Commutative Groups
• Makanin-Razborov Diagrams over Free Products

Cited by in corpus (1)

• Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups