On Systems of Equations over Free Products of Groups

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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

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Group Theory, Logic, 20F10 (Primary) 20E06 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/223119

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.2096
 http://arxiv.org/abs/0903.2096

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arXiv