On Systems of Equations over Free Products of Groups

Details On Systems of Equations over Free Products of Groups On Systems of Equations over Free Products of Groups

2009-03-12

arxiv.org/abs/0903.2096v1

Mathematics

Group Theory

71 pages, 13 figures

Scientific paper

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.

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