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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Equations in free groups
are not finitely approximable


Authors: Thierry Coulbois and Anatole Khelif
Journal: Proc. Amer. Math. Soc. 127 (1999), 963-965
MSC (1991): Primary 20F10, 03B25, 20E18
MathSciNet review: 1485465
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Abstract: We give an equation in any free group $F$ of rank $\geq 2$ that has a solution in any finite quotient of $F$, but has no solution in $F$.


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Additional Information

Thierry Coulbois
Affiliation: Equipe de Logique, UFR de Mathematiques, Universite Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France

Anatole Khelif
Affiliation: Equipe de Logique, UFR de Mathematiques, Universite Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04747-4
PII: S 0002-9939(99)04747-4
Received by editor(s): July 15, 1997
Additional Notes: The authors wish to thank G. Sabbagh for suggesting this question to them.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society