Vol. 56, No. 4, pp. 409-417 (1999)
Sur Certains Systèmes d'Équations avec Contraintes dans Un Groupe Libre
Jorge Almeida and Manuel DelgadoCentro de Matemática, Faculdade de Ciências da Universidade do Porto,
P. Gomes Teixeira, 4050 Porto - PORTUGAL
Abstract: The main theorem found by Ash in his proof of the type II conjecture is reformulated in terms of the solvability in the free group $F$ of systems of equations of the form $x\,y=z$ (where $y$ appears only once) with constraints given by subsets of the form $g\,H_1\cdots H_n$ where $g\in F$ and the $H_i$ are subgroups of $F$. More precisely, if such a system has no solution for finitely generated subgroups $H_i$, then one may replace each $H_i$ by a subgroup of finite index containing it so that the system remains without solution.
Keywords: Free group; equation; profinite topology; relational morphism; labeled graph; free monoid; finite monoid; pseudovariety.
Classification (MSC2000): 20M07, 20E18, 20E10.
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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.