Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Equations in free groups are not finitely approximable

Author(s): Thierry Coulbois; Anatole Khelif
Journal: Proc. Amer. Math. Soc. 127 (1999), 963-965.
MSC (1991): Primary 20F10, 03B25, 20E18
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

1.
G. Baumslag, Residual nilpotency and relations in free groups, J. of Algebra 2 (1965) 271-282. MR 31:3487

2.
B. Hartley, Subgroups of finite index in profinite groups, Mathematische Zeitschrift 168 (1979) 71-76. MR 80k:20028

3.
A. Khelif, Some properties of free groups and their profinite completions, in preparation.

4.
G.S. Makanin, Equations in a free group, Math. USSR Izv. 21 (1983) 483-546. MR 84m:20040

5.
C. Martinez, On power subgroups of profinite groups , Trans. of the A. M. S. 345 (1994) 865-869. MR 95d:20053

6.
M.P. Schützenberger, Sur l'equation $a^{2+n}= b^{2+m}c^{2+p}$ dans un groupe libre, Comptes Rend. de l'Ac. des Sciences (Paris) 248 (1959) 2435-2436. MR 21:2000

7.
M.R. Vaughan-Lee, The restricted Burnside problem, London Math. Soc., Oxford 1990. MR 92c:20001

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F10, 03B25, 20E18

Retrieve articles in all Journals with MSC (1991): 20F10, 03B25, 20E18

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: 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
Copyright of article: Copyright 1999, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google