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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

Abstract

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.

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Eric Jaligot. Zlil Sela. "Makanin–Razborov diagrams over free products." Illinois J. Math. 54 (1) 19 - 68, Spring 2010. https://doi.org/10.1215/ijm/1299679737

Information

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

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

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

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

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Vol.54 • No. 1 • Spring 2010
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