Open Access
Translator Disclaimer
Spring 2010 Makanin–Razborov diagrams over free products
Eric Jaligot, Zlil Sela
Illinois J. Math. 54(1): 19-68 (Spring 2010). DOI: 10.1215/ijm/1299679737


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.


Download Citation

Eric Jaligot. Zlil Sela. "Makanin–Razborov diagrams over free products." Illinois J. Math. 54 (1) 19 - 68, Spring 2010.


Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1252.20043
MathSciNet: MR2776984
Digital Object Identifier: 10.1215/ijm/1299679737

Primary: 20F65
Secondary: 03B35 , 20E05 , 20F10

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign


Vol.54 • No. 1 • Spring 2010
Back to Top