Equations in free groups are not finitely approximable
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- by Thierry Coulbois and Anatole Khelif
- Proc. Amer. Math. Soc. 127 (1999), 963-965
- DOI: https://doi.org/10.1090/S0002-9939-99-04747-4
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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 $F$.References
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Bibliographic 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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 963-965
- MSC (1991): Primary 20F10, 03B25, 20E18
- DOI: https://doi.org/10.1090/S0002-9939-99-04747-4
- MathSciNet review: 1485465