Makanin-razborov diagrams over free products

Eric Jaligot*, Zlil Sela

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper is the first in a sequence on the first order theory of free products and further generalizations. In the first paper, we generalize the analysis of systems of equations over free and (torsion-free) hyperbolic groups, and analyze systems of equations over free products. To do that we introduce limit groups over the class of free products, and show that a finitely presented group has a canonical (finite) collection of maximal limit quotients. We further extend this finite collection and associate a Makanin-Razborov diagram over free products with every f.p. group. This MR diagram encodes all the quotients of a given f.p. group that are free products, all its homomorphisms into free products, and equivalently all the solutions to a given system of equations over a free product.

Original languageAmerican English
Pages (from-to)19-68
Number of pages50
JournalIllinois Journal of Mathematics
Issue number1
StatePublished - 2010


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